CS 4220: Numerical Analysis

Introduction

David Bindel

2026-01-21

Welcome!

CS 4220/5223 + Math 4260:
Numerical Analysis: Linear and Nonlinear Problems

https://www.cs.cornell.edu/courses/cs4220/2026sp/

Topics

  • Complements CS 4210 / Math 4250
  • Two parts:
    • Numerical linear algebra (linear systems, least squares, eigenstuff)
    • Nonlinear equation solving and continuous optimization

Learning outcomes

  • Analyze sources of error
  • Choose appropriate NLA algorithms
  • Formulate nonlinear equations and optimization problems for solution
  • Analyze local convergence of nonlinear solvers
  • Reason about global convergence of nonlinear solvers
  • Use numerical methods to solve practical problems

Themes: Correctness

  • Know the answer in advance
  • Draw a picture
  • Document, test, and check for errors
  • Build modules and know how they compose
  • Problem formulation and representation matters!
  • Plan convergence monitoring and stopping criteria
  • Avoid numerical anti-patterns

Themes: Performance

  • Time and memory scaling
  • Knowing how to design for speed (and what should be fast)
  • Understand performance tradeoffs in iterations
  • Use of approximations and surrogages

Prerequisites

  • Linear algebra and multivariate calculus
  • Programming knowledge
    • Assume you can pick up Julia
  • “Sufficient mathematical maturity”

Enrollment logistics

  • There should be plenty of room!
  • Add yourself to the waitlist to get in
  • PIN distribution is managed by Bowers student services (not me)

Class meetings

  • We will not exactly replicate notes (or videos)
  • Some experiments: lecture plus
    • Live coding exercises
    • Small group activities
  • Please give feedback on what works or doesn’t!
  • If you have to miss, ask a friend for notes

Homework and projects

  • Six solo 1-week homeworks (Monday to Monday)
    • Mix of short answers, plots, computations, proofs
  • Three 2-week projects (small group)
    • Longer and on a theme
  • Paper project for 5223 students
  • Up to three slip days per assignment (six total)

Exams

  • Oral midterm (10 minutes standard)
    • Will run in March on a rolling basis
  • In-person final exam

Collaboration

  • Cite what you use and acknowledge if you got help
    • From a book or article
    • From the TA
    • From a peer
    • From some online resource
  • Stick to general discussion (except with partner on a project)

Grading: 4220/4260

  • Homework: 6% times 5 homeworks (best of 6)
  • Projects: 10% times 3 projects
  • Midterm (oral): 10%
  • Final: 30%

Grading: 5223

  • Homework: 5% times 5 homeworks (best of 6)
  • Paper project: 5%
  • Projects: 10% times 3 projects
  • Midterm (oral): 10%
  • Final: 30%

AI tools

  • May: search, explore and review, and practice course concepts
    • But the summaries aren’t always right!
    • Don’t be too credulous – if you are, it’s on you
  • May not: use AI for writing code or solutions
    • It’s hard for us to check this
    • But we can ask you to come by and explain your solution

Academic integrity

  • If you are in a jam, talk to us
    • We can help you plan
    • This is easiest if you ask early!
  • When in doubt, cite