Preface to the Third Edition

The field of matrix computations continues to grow and mature. In the Third Edition we have added over 300 new references and 100 new problems. The LINPACK and EISPACK citations have been replaced with appropriate pointers to LAPACK with key codes tabulated at the  beginning of appropriate chapters.

In the First Edition and Second Edition we identified a small number of global references: Wilkinson (1965), Forsythe and Moler (1967), Stewart (1973), Hanson and Lawson (1974) and Parlett (1980). These volumes are as important as ever to the research landscape, but there are some magnificent new textbooks and monographs on the scene.

We continue as before with the practice of giving references at the end of each section and a master bibliography at the end of the book.

The earlier editions suffered from a large number of typographical errors and we are obliged to the dozens of readers who have brought these to our attention. Many corrections and clarifications have been made.

Here are some specific highlights of the new edition. Chapter 1 (Matrix Multiplication Problems) and Chapter 6 (Parallel Matrix Computations) have been completely rewritten with less formality. We think that this facilitates the building of intuition for high performance computing and draws a better line between algorithm and implementation on the printed page.

In Chapter 2 (Matrix Analysis) we expanded the treatment of CS decomposition and included a proof. The overview of floating point arithmetic has been brought up to date. In Chapter 4 (Special Linear Systems) we embellished the Toeplitz section with connections to circulant matrices and the fast Fourier transform. A subsection on equilibrium systems has been included in our treatment of indefinite systems.

A more accurate rendition of the modified Gram-Schmidt process is offered in Chapter 5 (Orthogonalization and Least Squares). Chapter 8 (The Symmetric Eigenproblem) has been extensively rewritten and rearranged so as to minimize its dependence upon Chapter 7 (The Unsymmetric Eigenproblem). Indeed, the coupling between these two chapters is now so minimal that it is possible to read either one first.

In Chapter 9 (Lanczos Methods) we have expanded the discussion of the unsymmetric Lanczos process and the Arnoldi iteration. The unsymmetric component'' of Chapter 10 (Iterative Methods for Linear Systems) has likewise been broadened with a whole new section devoted to various Krylov space methods designed to handle the sparse unsymmetric linear system problem.

In Section 12.5 (Updating Orthogonal Decompositions) we included a new subsection on ULV updating. Toeplitz matrix eigenproblems and orthogonal matrix eigenproblems are discussed in Section 12.6.

Both of us look forward to continuing the dialog with our readers. As we said in the Preface to the {\em Second Edition}, It has been a pleasure to deal with such an interested and friendly readership.''

Many individuals made valuable Third Edition suggestions, but Greg Ammar, Mike Heath, Nick Trefethen, and Steve Vavasis deserve special thanks.

Finally, we would like to acknowledge the support of Cindy Robinson at Cornell. A dedicated assistant makes a big difference.