**| Books |
Papers | Research |
Biographical | Home
|**

Useful books that collectively cover the field, are cited below. Chapter titles are included if appropriate but do not infer too much from the level of detail because one author's chapter may be another's subsection. The citations are classified as follows:

**Pre-1970 Classics.**Early volumes that set the stage.**Introductory (General).**Suitable for the undergraduate classroom.**Advanced (General).**Best for practitioners and graduate students.**Analytical.**For the supporting mathematics.**Linear Equation Problems.**Ax=b**Linear Fitting Problems.**||Ax - b||_{2}.**Eigenvalue Problems.**Ax = lambda x.**High Performance.**Parallel/vector issues.**Edited Volumes.**Useful, thematic collections.

Within each group the entries are specified in chronological order.

V.N. Faddeeva (1959). *Computational Methods of Linear Algebra*,
Dover, New York.

Basic Material from Linear Algebra. Systems of Linear Equations. The Proper Numbers and Proper Vectors of a Matrix.

E. Bodewig (1959). *Matrix Calculus*, North Holland, Amsterdam.

Matrix Calculus. Direct Methods for Linear Equations. Indirect Methods for Linear Equations. Inversion of Matrices. Geodetic Matrices. Eigenproblems.

R.S. Varga (1962). *Matrix Iterative Analysis*, Prentice-Hall,
Englewood Cliffs, NJ.

Matrix Properties and Concepts. Nonnegative Matrices. Basic Iterative Methods and Comparison Theorems. Successive Overrelaxation Iterative Methods. Semi-Iterative Methods. Derivation and Solution of Elliptic Difference Equations. Alternating Direction Implicit Iterative Methods. Matrix Methods for Parabolic Partial Differential Equations. Estimation of Acceleration Parameters.

J.H. Wilkinson (1963). *Rounding Errors in Algebraic Processes*,
Prentice-Hall, Englewood Cliffs, NJ.

The Fundamental Arithmetic Operations. Computations In solving Polynomials. Matrix Computations.

A.S. Householder (1964). *Theory of Matrices in Numerical Analysis*,
Blaisdell, New York. Reprinted in 1974 by Dover, New York.

Some Basic Identities and Inequalities. Norms, Bounds, and Convergence. Localization Theorems and Other Inequalities. The Solution of Linear Systems: Methods of Successive Approximation. Direct Methods of Inversion. Proper Values and Vectors: Normalization and Reduction of the Matrix. Proper Values and Vectors: Successive Approximation.

L. Fox (1964). *An Introduction to Numerical Linear Algebra*,
Oxford University Press, Oxford, England.

Introduction, Matrix Algebra. Elimination Methods of Gauss, Jordan, and Aitken. Compact Elimination Methods of Doolittle, Crout, Banachiewicz, and Cholesky. Orthogonalization Methods. Condition, Accuracy, and Precision. Comparison of Methods, Measure of Work. Iterative and Gradient Methods. Iterative methods for Latent Roots and Vectors. Transformation Methods for Latent Roots and Vectors. Notes on Error Analysis for Latent Roots and Vectors.

J.H. Wilkinson (1965). *The Algebraic Eigenvalue Problem,*
Clarendon Press, Oxford, England.

Theoretical Background. Perturbation Theory. Error Analysis. Solution of Linear Algebraic Equations. Hermitian Matrices. Reduction of a General Matrix to Condensed Form. Eigenvalues of Matrices of Condensed Forms. The LR and QR Algorithms. Iterative Methods.

G.E. Forsythe and C. Moler (1967). *Computer Solution of Linear
Algebraic Systems,* Prentice-Hall, Englewood Cliffs, NJ.

Reader's Background and Purpose of Book. Vector and Matrix Norms. Diagonal Form of a Matrix Under Orthogonal Equivalence. Proof of Diagonal Form Theorem. Types of Computational Problems in Linear Algebra. Types of Matrices encountered in Practical Problems. Sources of Computational Problems of Linear Algebra. Condition of a Linear System. Gaussian Elimination and LU Decomposition. Need for Interchanging Rows. Scaling Equations and Unknowns. The Crout and Doolittle Variants. Iterative Improvement. Computing the Determinant. Nearly Singular Matrices. Algol 60 Program. Fortran, Extended Algol, and PL/I Programs. Matrix Inversion. An Example: Hilbert Matrices. Floating Point Round-Off Analysis. Rounding Error in Gaussian Elimination. Convergence of Iterative Improvement. Positive Definite Matrices; Band Matrices. Iterative Methods for Solving Linear Systems. Nonlinear Systems of Equations.

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A.R. Gourlay and G.A. Watson (1973). *Computational Methods for
Matrix Eigenproblems*, John Wiley & Sons, New York.

Introduction. Background Theory. Reductions and Transformations. Methods for the Dominant Eigenvalue. Methods for the Subdominant Eigenvalue. Inverse Iteration. Jacobi's Methods. Givens and Householder's Methods. Eigensystem of a Symmetric Tridiagonal Matrix. The LR and QR Algorithms. Extensions of Jacobi's Method. Extension of Givens' and Householder's Methods. QR Algorithm for Hessenberg Matrices. generalized Eigenvalue Problems. Available Implementations.

G.W. Stewart (1973). *Introduction to Matrix Computations,*
Academic Press, New York.

Preliminaries. Practicalities. The Direct Solution of Linear Systems. Norms, Limits, and Condition Numbers. The Linear Least Squares Problem. Eigenvalues and Eigenvectors. The QR Algorithm.

R.J. Goult, R.F. Hoskins, J.A. Milner and M.J. Pratt
(1974). *Computational Methods in Linear Algebra*, John Wiley and Sons, New York.

Eigenvalues and Eigenvectors. Error Analysis. The Solution of Linear Equations by Elimination and Decomposition Methods. The Solution of Linear Systems of Equations by Iterative Methods. Errors in the Solution Sets of Equations. Computation of Eigenvalues and Eigenvectors. Errors in Eigenvalues and Eigenvectors. Appendix -- A Survey of Essential Results from Linear Algebra.

T.F. Coleman and C.F. Van Loan (1988). *Handbook for
Matrix Computations*, SIAM Publications, Philadelphia, PA.

Fortran 77, The Basic Linear Algebra Subprograms, Linpack, Matlab.

W.W. Hager (1988). *Applied Numerical Linear Algebra,*
Prentice-Hall, Englewood Cliffs, NJ.

Introduction. Elimination Schemes. Conditioning. Nonlinear Systems. Least Squares. Eigenproblems. Iterative Methods.

P.G. Ciarlet (1989). *Introduction to Numerical
Linear Algebra and Optimisation*, Cambridge University Press.

A Summary of Results on Matrices. General Results in the Numerical Analysis of Matrices. Sources of Problems in the Numerical Analysis of Matrices. Direct Methods for the Solution of Linear Systems. Iterative Methods for the Solution of Linear Systems. Methods for the Calculation of Eigenvalues and Eigenvectors. A Review of Differential Calculus. Some Applications. General Results on Optimization. Some Algorithms. Introduction to Nonlinear Programming. Linear Programming.

D.S. Watkins (1991). *Fundamentals of Matrix
Computations*, John Wiley and Sons, New York.

Gaussian Elimination and Its Variants. Sensitivity of Linear Systems; Effects of Roundoff Errors. Orthogonal Matrices and the Least-Squares Problem. Eigenvalues and Eigenvectors I. Eigenvalues and Eigenvectors II. Other Methods for the Symmetric Eigenvalue Problem. The Singular Value Decomposition.

P. Gill, W. Murray, and M.H. Wright (1991). *Numerical
Linear Algebra and Optimization, Vol. 1*, Addison-Wesley, Reading, MA.

Introduction. Linear Algebra Background. Computation and Condition. Linear Equations. Compatible Systems. Linear Least Squares. Linear Constraints I: Linear Programming. The Simplex Method.

A. Jennings and J.J. McKeowen (1992). *Matrix
Computation (2nd ed)*, John Wiley and Sons, New York.

Basic Algebraic and Numerical Concepts. Some Matrix Problems. Computer Implementation. Elimination Methods for Linear Equations. Sparse Matrix Elimination. Some Matrix Eigenvalue Problems. Transformation Methods for Eigenvalue Problems. Sturm Sequence Methods. Vector Iterative Methods for Partial Eigensolution. Orthogonalization and Re-Solution Techniques for Linear Equations. Iterative Methods for Linear Equations. Non-linear Equations. Parallel and Vector Computing.

B.N. Datta (1995). *Numerical Linear Algebra and
Applications*. Brooks/Cole Publishing Company, Pacific Grove, California.

Review of Required Linear Algebra Concepts. Floating Point Numbers and Errors in Computations. Stability of Algorithms and Conditioning of Problems. Numerically Effective Algorithms and Mathematical Software. Some Useful Transformations in Numerical Linear Algebra and Their Applications. Numerical Matrix Eigenvalue Problems. The Generalized Eigenvalue Problem. The Singular Value Decomposition. A Taste of Roundoff Error Analysis.

M.T. Heath (1997). *Scientific Computing: An
Introductory Survey*, McGraw-Hill, New York.

Scientific Computing. Systems of Linear Equations. Linear Least Squares. Eigenvalues and Singular Values. Nonlinear Equations. Optimization. Interpolation. Numerical Integration and Differentiation. Initial Value Problems for ODEs. Boundary Value Problems for ODEs. Partial Differential Equations. Fast Fourier Transform. Random Numbers and Simulation.

C.F. Van Loan (1997). *Introduction to Scientific
Computing: A Matrix-Vector Approach Using Matlab*, Prentice Hall, Upper Saddle River,
NJ.

Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem.

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N.J. Higham (1996). *Accuracy and Stability of
Numerical Algorithms*, SIAM Publications, Philadelphia, PA.

Principles of Finite Precision Computation. Floating Point Arithmetic. Basics. Summation. Polynomials. Norms. Perturbation Theory for Linear Systems. Triangular Systems. LU Factorization and Linear Equations. Cholesky Factorization. Iterative Refinement. Block LU Factorization. Matrix Inversion. Condition Number Estimation. The Sylvester Equation. Stationary Iterative Methods. Matrix Powers. QR Factorization. The Least Squares Problem. Underdetermined Systems. Vandermonde Systems. Fast Matrix Multiplication. The Fast Fourier Transform and Applications. Automatic Error Analysis. Software Issues in Floating Point Arithmetic. A Gallery of Test Matrices.

J.W. Demmel (1996). *Numerical Linear Algebra*,
SIAM Publications, Philadelphia, PA.

Introduction. Linear Equation Solving. Linear Least Squares Problems. Nonsymmetric Eigenvalue Problems. The Symmetric Eigenproblem and Singular Value Decomposition. Iterative Methods for Linear Systems and Eigenvalue Problems. Iterative Algorithms for Eigenvalue Problems.

L.N. Trefethen and D. Bau III (1997). *Numerical
Linear Algebra*, SIAM Publications, Philadelphia, PA.

Matrix-Vector Multiplication. Orthogonal Vectors and Matrices. Norms. The Singular Value Decomposition. More on the SVD. Projectors. QR Factorization. Gram-Schmidt Orthogonalization. Matlab. Householder Triangularization. Least-Squares Problems. Conditioning and Condition Numbers. Floating Point Arithmetic. Stability. More on Stability. Stability of Householder Triangularization. Stability of Back Substitution. Conditioning of Least-Squares Problems. Stability of Least-Squares Algorithms. Gaussian Elimination. Pivoting. Stability of Gaussian Elimination. Cholesky Factorization. Eigenvalue Problems. Overview of Eigenvalue Algorithms. Reduction to Hessenberg/Tridiagonal Form. Rayleigh Quotient, Inverse Iteration. QR Algorithm Without Shifts. QR Algorithm With Shifts. Other Eigenvalue Algorithms. Computing the SVD. Overview of Iterative Methods. The Arnoldi Iteration. How Arnoldi Locates Eigenvalues. GMRES. The Lanczos Iteration. Orthogonal Polynomials and Gauss Quadrature. Conjugate Gradients. Biorthogonalization Methods. Preconditioning. The Definition of Numerical Analysis.

F.R. Gantmacher (1959). *The Theory of Matrices Vol.
1*, Chelsea, New York.

Matrices and Operations on Matrices. The Algorithm of Gauss and Some of its Applications. Linear Operators in an n-dimensional Vector Space. The Characteristic Polynomial and the Minimum Polynomial of a Matrix. Functions of Matrices, Equivalent Transformations of Polynomial Matrices, Analytic Theory of Elementary Divisors. The Structure of a Linear Operator in an n-dimensional Space. Matrix Equations. Linear Operators in a Unitary Space. Quadratic and Hermitian Forms.

F.R. Gantmacher (1959). *The Theory of Matrices Vol.
2*, Chelsea, New York.

Complex Symmetric, Skew-Symmetric, and Orthogonal Matrices. Singular Pencils of Matrices. Matrices with Nonnegative Elements. Application of the Theory of Matrices to the Investigation of Systems of Linear Differential Equations. The Problem of Routh-Hurwitz and Related Questions.

A. Berman and R.J. Plemmons (1979). *Nonnegative
Matrices in the Mathematical Sciences*, Academic Press, New York. Reprinted with
additions in 1994 by SIAM Publications, Philadelphia, PA.

Matrices Which Leave a Cone Invariant. Nonnegative Matrices. Semigroups of Nonnegative Matrices. Symmetric Nonnegative Matrices. Generalized Inverse-Positivity. M-Matrices. Iterative Methods for Linear Systems. Finite Markov Chains. Input-Output Analysis in Economics. The Linear Complementarity Problem.

G.W. Stewart and J. Sun (1990). *Matrix Perturbation
Theory*, Academic Press, San Diego.

Preliminaries. Norms and Metrics. Linear Systems and Least Squares Problems. The Perturbation of Eigenvalues. Invariant Subspaces. Generalized Eigenvalue Problems.

R. Horn and C. Johnson (1985). *Matrix Analysis*,
Cambridge University Press, New York.

Review and Miscellanea. Eigenvalues, Eigenvectors, and Similarity. Unitary Equivalence and Normal Matrices. Canonical Forms. Hermitian and Symmetric Matrices. Norms for Vectors and Matrices. Location and Perturbation of Eigenvalues. Positive Definite Matrices.

R. Horn and C. Johnson (1991). *Topics in Matrix
Analysis*, Cambridge University Press, New York.

The Field of Values. Stable Matrices and Inertia. Singular Value Inequalities. Matrix Equations and the Kronecker Product. The Hadamard Product. Matrices and Functions.

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D.M. Young (1971). *Iterative Solution of Large
Linear Systems*, Academic Press, New York.

Introduction. Matrix Preliminaries. Linear Stationary Iterative Methods. Convergence of the Basic Iterative Methods. Eigenvalues of the SOR Method for Consistently Ordered Matrices. Determination of the Optimum Relaxation Parameter. Norms of the SOR Method. The Modified SOR Method: Fixed Parameters. Nonstationary Linear Iterative Methods. The Modified SOR Method: Variable Parameters. Semi-Iterative Methods. Extensions of the SOR Theory; Stieltjes Matrices. Generalized Consistently Ordered Matrices. Group Iterative Methods. Symmetric SOR Method and Related Methods. Second Degree Methods. Alternating Direction Implicit Methods. Selection of an Iterative Method.

L.A. Hageman and D.M. Young (1981). *Applied
Iterative Methods*, Academic Press, New York.

Background on Linear Algebra and Related Topics. Background on Basic Iterative Methods. Polynomial Acceleration. Chebyshev Acceleration. An Adaptive Chebyshev Procedure Using Special Norms. Adaptive Chebyshev Acceleration. Conjugate Gradient Acceleration. Special Methods for Red/Black Partitionings. Adaptive Procedures for Successive Overrelaxation Method. The Use of Iterative Methods in the Solution of Partial Differential Equations. Case Studies. The Nonsymmetrizable Case.

A. George and J. W-H. Liu (1981). *Computer Solution
of Large Sparse Positive Definite Systems*. Prentice-Hall Inc., Englewood Cliffs, New
Jersey.

Introduction. Fundamentals. Some Graph Theory Notation and Its Use in the Study of Sparse Symmetric Matrices. BAnd and Envelope Methods. General Sparse Methods. Quotient Tree Methods for Finite Element and Finite Difference Problems. One-Way Dissection Methods for Finite Element Problems. Nested Dissection Methods. Numerical Experiments.

S. Pissanetsky (1984). *Sparse Matrix Technology*,
Academic Press, New York.

Fundamentals. Linear Algebraic Equations. Numerical Errors in Gaussian Elimination. Ordering for Gauss Elimination: Symmetric Matrices. Ordering for Gauss Elimination: General Matrices. Sparse Eigenanalysis. Sparse Matrix Algebra. Connectivity and Nodal Assembly. General Purpose Algorithms.

I.S. Duff, A.M. Erisman, and J.K. Reid (1986). *Direct
Methods for Sparse Matrices,* Oxford University Press, New York.

Introduction. Sparse Matrices:Storage Schemes and Simple Operations. Gaussian Elimination for Dense Matrices: The Algebraic Problem. Gaussian Elimination for Dense Matrices: Numerical Considerations. Gaussian Elimination for Sparse Matrices: An Introduction. Reduction to Block Triangular Form. Local Pivotal Strategies for Sparse Matrices. Ordering Sparse Matrices to Special Forms. Implementing Gaussian Elimination: Analyse with Numerical Values. Implementing Gaussian Elimination with Symbolic Analyse. Partitioning, Matrix Modification, and Tearing. Other Sparsity-Oriented Issues.

R. Barrett, M. Berry, T.F. Chan, J. Demmel, J. Donato,
J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst (1993). *Templates for
the Solution of Linear Systems: Building Blocks for Iterative Methods*, SIAM
Publications, Philadelphia, PA.

Introduction. Why Use Templates? What Methods are Covered? Iterative Methods. Stationary Methods. Nonstationary Iterative Methods. Survey of Recent Krylov Methods. Jacobi, Incomplete, SSOR, and Polynomial Preconditioners. Complex Systems. Stopping Criteria. Data Structures. Parallelism. The Lanczos Connection. Block Iterative Methods. Reduced System Preconditioning. Domain Decomposition Methods. Multigrid Methods. Row Projection Methods.

W. Hackbusch (1994). *Iterative Solution of Large
Sparse Systems of Equations*, Springer-Verlag, New York.

Introduction. Recapitulation of Linear Algebra. Iterative Methods. Methods of Jacobi and Gauss-Seidel and SOR Iteration in the Positive Definite Case. Analysis in the 2-Cyclic Case. Analysis for M-Matrices. Semi-Iterative Methods. Transformations, Secondary Iterations, Incomplete Triangular Decompositions. Conjugate Gradient Methods. Multi-Grid Methods. Domain Decomposition Methods.

O. Axelsson (1994). *Iterative Solution Methods*,
Cambridge University Press.

Direct Solution Methods. Theory of Matrix Eigenvalues. Positive Definite Matrices, Schur Complements, and Generalized Eigenvalue Probems. Reducible and Irreducible Matrices and the Perron-Frobenious Theory for Nonnegative Matrices. Basic Iterative Methods and Their Rates of Convergence. M-Matrices, Convergent Splittings, and the SOR Method. Incomplete Factorization Preconditioning Methods. Approximate Matrix Inverses and Corresponding Preconditioning Methods. Block Diagonal and Schur Complement Preconditionngs. Estimates of Eigenvalues and Condition Numbers for Preconditioned Matrices. Conjugate Gradient and Lanczos-Type Methods. Generalized Conjugate Gradient Methods. The Rate of Convergence of the Conjugate Gradient Method.

Y. Saad (1996). *Iterative Methods for Sparse Linear
Systems*, PWS Publishing Co., Boston.

Background in Linear Algebra. Discretization of PDEs. Sparse Matrices. Basic Iterative Methods. Projection Methods. Krylov Subspace Methods -- Part I. Krylov Subspace Methods -- Part II. Methods Related to the Normal Equations. Preconditioned Iterations. Preconditioning Techniques. Parallel Implementations. Parallel Preconditioners. Domain Decomposition Methods.

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C.L. Lawson and R.J. Hanson (1974). *Solving Least
Squares Problems*, Prentice-Hall, Englewood Cliffs, NJ. Reprinted with a detailed ``new
developments'' appendix in 1996 by SIAM Publications, Philadelphia, PA.

Introduction. Analysis of the Least Squares Problem. Orthogonal Decomposition by Certain Elementary Transformations. Orthogonal Decomposition by Singular Value Decomposition. Perturbation Theorems for Singular Values. Bounds for the Condition Number of a Triangular Matrix. The Pseudoinverse. Perturbation Bounds for the Pseudoinverse. Perturbation Bounds for the Solution of Problem LS. Numerical Computations Using Elementary Orthogonal Transformations. Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem. Computation of the Covariance Matrix of the Solution Parameters. Computing the Solution for the Underdetermined Full Rank Problem. Computing the Solution for Problem LS with Possibly Deficient Pseudorank. Analysis of Computing Errors for Householder Transformations. Analysis of Computing Errors for the Problem LS. Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic. Computation of the Singular Value Decomposition and the Solution of Problem LS. Other Methods for Least Squares Problems. Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space. Linear Least Squares with Linear Equality Constraints by Direct Elimination. Linear Least Squares with Linear Equality Constraints by Weighting. Linear least Squares with Linear Inequality Constraints. Modifying a QR Decomposition to Add or Remove Column Vectors. Practical Analysis of Least Squares Problems. Examples of Some Methods of Analyzing a Least Squares Problem. Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix.

R.W. Farebrother (1987). *Linear Least Squares
Computations*, Marcel Dekker, New York.

The Gauss and Gauss--Jordan Methods. Matrix Analysis of Gauss's Method: The Cholesky and Doolittle Decompositions. The Linear Algebraic Model: The Method of Averages and the Method of Least Squares. The Cauchy-Bienayme, Laplace, and Schmidt Procedures. Householder Procedures. Givens Procedures. Updating the QU Decomposition. Pseudorandom Numbers. The Standard Linear Model. Condition Numbers. Instrumental Variable Estimators. Generalized Least Squares Estimation. Iterative Solutions of Linear and Nonlinear Least Squares Problems. Canonical Expressions for the Least Squares Estimators and Test Statistics. Traditional Expressions for the Least Squares Updating Formulas and test Statistics. Least Squares Estimation Subject to Linear Constraints.

S. Van Huffel and J. Vandewalle (1991). *The Total
Least Squares Problem: Computational Aspects and Analysis*, SIAM Publications,
Philadelphia, PA.

Introduction. Basic Principles of the Total Least Squares Problem. Extensions of the Basic Total Least Squares Problem. Direct Speed Improvement of the Total Least Squares Computations. Iterative Speed Improvement for Solving Slowly Varying Total Least Squares Problems. Algebraic Connections Between Total Least Squares and Least Squares Problems. Sensitivity Analysis of Total Least Squares and Least Squares Problems in the Presence of Errors in All Data. Statistical Properties of the Total Least Squares Problem. Algebraic Connections Between Total Least Squares Estimation and Classical Linear Regression in Multicollinearity Problems. Conclusions.

A. Bjorck (1996). *Numerical Methods for Least
Squares Problems,* SIAM Publications, Philadelphia, PA.

Mathematical and Statistical Properties of Least Squares Solutions. Basic Numerical Methods. Modified Least Squares Problems. Generalized Least Squares Problems. Constrained Least Squares Problems. Direct Methods for Sparse Least Squares Problems. Iterative Methods for Least Squares Problems. Least Squares with Special Bases. Nonlinear Least Squares Problems.

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B.N. Parlett (1980). *The Symmetric Eigenvalue
Problem,* Prentice-Hall, Englewood Cliffs, NJ.

Basic Facts about Self-Adjoint Matrices. Tasks, Obstacles, and Aids. Counting Eigenvalues. Simple Vector Iterations. Deflation. Useful Orthogonal Matrices. Tridiagonal Form. The QL and QR Algorithms. Jacobi Methods. Eigenvalue Bounds. Approximation from a Subspace. Krylov Subspaces. Lanczos Algorithms. Subspace Iteration. The General Linear Eigenvalue Problem.

J. Cullum and R.A. Willoughby (1985a). *Lanczos
Algorithms for Large Symmetric Eigenvalue Computations, Vol. I Theory,* Birkhauser,
Boston.

Preliminaries: Notation and Definitions. Real Symmetric Problems. Lanczos Procedures, Real Symmetric Problems. Tridiagonal Matrices. Lanczos Procedures with No Reorthogonalization for Symmetric Problems. Real Rectangular Matrices. Non-Defective Complex Symmetric Matrices. Block Lanczos Procedures, Real Symmetric Matrices.

J. Cullum and R.A. Willoughby (1985b). *Lanczos
Algorithms for Large Symmetric Eigenvalue Computations, Vol. II Programs,* Birkhauser,
Boston.

Lanczos Procedures. Real Symmetric Matrices. Hermitian Matrices. Factored Inverses of Real Symmetric Matrices. Real Symmetric Generalized Problems. Real Rectangular Problems. Nondefective Complex Symmetric Matrices. Real Symmetric Matrices, Block Lanczos Code. Factored Inverses, Real Symmetric Matrices, Block Lanczos Code.

Y. Saad (1992). *Numerical Methods for Large
Eigenvalue Problems: Theory and Algorithms*, John Wiley and Sons, New York.

Background in Matrix Theory and Linear Algebra. Perturbation Theory and Error Analysis. The Tools of Spectral Approximation. Subspace Iteration. Krylov Subspace Methods. Acceleration Techniques and Hybrid Methods. Preconditioning Techniques. Non-Standard Eigenvalue Problems. Origins of Matrix Eigenvalue Problems.

F. Chatelin (1993). *Eigenvalues of Matrices*,
John Wiley and Sons, New York.

Supplements from Linear Algebra. Elements of Spectral Theory. Why Compute Eigenvalues. Error Analysis. Foundations of Methods for Computing Eigenvalues. Numerical Methods for Large Matrices. Chebyshev's Iterative Methods.

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W. Schonauer (1987). *Scientific Computing on Vector
Computers,* North Holland, Amsterdam.

Introduction. The First Commercially Significant Vector Computer. The Arithmetic Performance of the First Commercially Significant Vector Computer. Hockney's n

^{1/2}and Timing Formulae. Fortran and Autovectorization. Behavior of Programs. Some Basic Algorithms, Recurrences. Matrix Operations. Systems of Linear Equations with Full Matrices. Tridiagonal Linear Systems. The Iterative Solution of Linear Equations. Special Applications. The Fujitsu VPs and Other Japanese Vector Computers. The Cray-2. The IBM VF and Other Vector Processors. The Convex C1.

R.W. Hockney and C.R. Jesshope (1988). *Parallel
Computers 2*, Adam Hilger, Bristol and Philadelphia.

Introduction. Pipelined Computers. Processor Arrays. Parallel Languages. Parallel Algorithms. Future Developments.

J.J. Modi (1988).* Parallel Algorithms and Matrix
Computation*, Oxford University Press, Oxford.

General Principles of Parallel Computing. Parallel Techniques and Algorithms. Parallel Sorting Algorithms. Solution of a System of Linear Algebraic Equations. The Symmetric Eigenvalue Problem: Jacobi's Method. QR Factorization. Singular Value Decomposition and Related Problems.

J. Ortega (1988). *Introduction to Parallel and
Vector Solution of Linear Systems*, Plenum Press, New York.

Introduction. Direct Methods for Linear Equations. Iterative Methods for Linear Equations.

J. Dongarra, I. Duff, D. Sorensen, and H. van der Vorst
(1990). *Solving Linear Systems on Vector and Shared Memory Computers,* SIAM
Publications, Philadelphia, PA.

Vector and Parallel Processing. Overview of Current High-Performance Computers. Implementation Details and Overhead. Performance Analysis, Modeling, and Measurements. Building Blocksin Linear Algebra. Direct Solution of Sparse Linear Systems. Iterative Solution of Sparse Linear Systems.

Y. Robert (1990). *The Impact of Vector and Parallel
Architectures on the Gaussian Elimination Algorithm*, Halsted Press, New York.

Introduction. Vector and Parallel Architectures. Vector Multiprocessor Computing. Hypercube Computing. Systolic Computing. Task Graph Scheduling. Analysis of Distributed Algorithms. Design Methodologies.

G.H. Golub and J.M. Ortega (1993). *Scientific
Computing: An Introduction with Parallel Computing,* Academic Press, Boston.

The World of Scientific Computing. Linear Algebra. Parallel and Vector Computing. Polynomial Approximation. Continuous Problems Solved Discretely. Direct Solution of Linear Equations. Parallel Direct Methods. Iterative Methods. Conjugate Gradient-Type Methods.

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D.J. Rose and R. A. Willoughby, eds. (1972). *Sparse
Matrices and Their Applications*, Plenum Press, New York, 1972

J.R. Bunch and D.J. Rose, eds. (1976). *Sparse Matrix
Computations*, Academic Press, New York.

I.S. Duff and G.W. Stewart, eds. (1979). *Sparse
Matrix Proceedings, 1978*, SIAM Publications, Philadelphia, PA.

I.S. Duff, ed. (1981). *Sparse Matrices and Their
Uses*, Academic Press, New York.

A. Bjorck, R.J. Plemmons, and H. Schneider, eds.
(1981). *Large-Scale Matrix Problems*, North-Holland, New York.

G. Rodrigue, ed. (1982). *Parallel Computation*,
Academic Press, New York.

B. Kagstrom and A. Ruhe, eds. (1983). *Matrix Pencils*,
Proc. Pite Havsbad, 1982, Lecture Notes in Mathematics 973, Springer-Verlag, New York and
Berlin.

J. Cullum and R.A. Willoughby, eds. (1986). *Large
Scale Eigenvalue Problems*, North-Holland, Amsterdam.

A. Wouk, ed. (1986). *New Computing Environments:
Parallel, Vector, and Systolic*, *SIAM Publications*, Philadelphia, PA.

M.T. Heath, ed. (1986). *Proceedings of First SIAM
Conference on Hypercube Multiprocessors*, SIAM Publications, Philadelphia, PA.

M.T. Heath, ed. (1987). *Hypercube Multiprocessors*,
SIAM Publications, Philadelphia, PA.

G. Fox, ed. (1988). *The Third Conference on
Hypercube Concurrent Computers and Applications, Vol. II -- Applications,* ACM Press,
New York.

M.H. Schultz, ed. (1988). *Numerical Algorithms for
Modern Parallel Computer Architectures*, IMA Volumes in Mathematics and Its
Applications, Number 13, Springer-Verlag, Berlin.

E.F. Deprettere, ed. (1988). *SVD and Signal
Processing*. Elsevier, Amsterdam.

B.N. Datta, C.R. Johnson. M.A. Kaashoek, R. Plemmons,
and E.D. Sontag, eds. (1988), *Linear Algebra in Signals, Systems, and Control,* SIAM
Publications, Philadelphia, PA.

J. Dongarra, I. Duff, P. Gaffney, and S. McKee, eds.
(1989), *Vector and Parallel Computing*, Ellis Horwood, Chichester, England.

O. Axelsson, ed. (1989). ``Preconditioned Conjugate
Gradient Methods,'' *BIT 29:4*.

K. Gallivan, M. Heath, E. Ng, J. Ortega, B. Peyton, R.
Plemmons, C. Romine, A. Sameh, and B. Voigt (1990), *Parallel Algorithms for Matrix
Computations*, SIAM Publications, Philadelphia, PA.

G.H. Golub and P. Van Dooren, eds. (1991). *Numerical
Linear Algebra, Digital Signal Processing, and Parallel Algorithms.* Springer-Verlag,
Berlin.

R. Vaccaro, ed. (1991). *SVD and Signal Processing
II: Algorithms, Analysis, and Applications*. Elsevier, Amsterdam.

R. Beauwens and P. de Groen, eds. (1992). *Iterative
Methods in Linear Algebra*, Elsevier (North-Holland), Amsterdam.

R.J. Plemmons and C.D. Meyer, eds. (1993). *Linear
Algebra, Markov Chains, and Queuing Models*, Springer-Verlag, New York.

M.S. Moonen, G.H. Golub, and B.L.R. de Moor, eds.
(1993). *Linear Algebra for Large Scale and Real-Time Applications*, Kluwer,
Dordrecht, The Netherlands.

J.D. Brown, M.T. Chu, D.C. Ellison, and R.J. Plemmons,
eds. (1994). *Proceedings of the Cornelius Lanczos International Centenary Conference*,
SIAM Publications, Philadelphia, PA.

R.V. Patel, A.J. Laub, and P.M. Van Dooren, eds.
(1994). *Numerical Linear Algebra Techniques for Systems and Control,* IEEE Press,
Piscataway, New Jersey.

J. Lewis, ed. (1994). *Proceedings of the Fifth SIAM
Conference on Applied Linear Algebra*, SIAM Publications, Philadelphia, PA.

A. Bojanczyk and G. Cybenko, eds. (1995). *Linear
Algebra for Signal Processing*, IMA Volumes in Mathematics and Its Applications,
Springer-Verlag, New York.

M. Moonen and B. De Moor, eds. (1995). *SVD and
Signal Processing III: Algorithms, Analysis, and Applications*. Elsevier, Amsterdam.

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