\( \newcommand\D{\mathrm{d}} \newcommand\E{\mathrm{e}} \newcommand\I{\mathrm{i}} \newcommand\bigOh{\mathcal{O}} \newcommand{\cat}[1]{\mathbf{#1}} \newcommand\curl{\vec{\nabla}\times} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\RR}{\mathbb{R}} \newcommand{\ZZ}{\mathbb{Z}} \)
UP | HOME

Numerical Analysis

Table of Contents

Numerical analysis is the blackest of the black arts. (Gerald Sussman)

1. Overview

The basic problem numerical analysis addresses: given some computation we want to perform in mathematics, how can we get the computer to do it? Specifically when we approximate real numbers by floating-point arithmetic, and we do not perform any symbolic manipulation.

2. References

  • Richard L. Burden and J. Douglas Faires, Numerical Analysis. 8th ed., Thomson, 2005.
  • David Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic". March 1991, eprint.
  • Peter Olver, Lecture notes on Numerical Analysis.

2.1. Numerical Differenial Equations

  • J. C. Butcher, Numerical Methods for Ordinary Differential Equations. 3rd Edition
  • David F. Griffiths, Desmond J. Higham, Numerical Methods for Ordinary Differential Equations: Initial Value Problems.

2.2. Theorem Provers and Numerical Analysis

  • Sylvie Boldo, Claude Marché, "Formal verification of numerical programs: from C annotated programs to mechanical proofs". Eprint, 2013, 18 pages.
  • Ruben Antonio Gamboa, "Mechanically Verifying Real-Valued Algorithms in ACL2". PhD thesis, U. Texas at Austin, PDF
  • David M Russinoff, Formal Verification of Floating-Point Hardware Design: A Mathematical Approach. Springer, 2018.

2.3. Numerical Linear Algebra

  • G.W. Stewart, Matrix Algorithms. 2 volumes
  • James Demmel, Applied Numerical Linear Algebra.
  • Trefethen and Bau, Numerical linear algebra.

Last Updated 2021-04-11 Sun 12:02.