Matrix Computations
by Gene H. Golub, Charles F. Van Loan · Johns Hopkins University Press
The standard graduate reference on matrix algorithms, presenting block algorithms, error and perturbation analysis for factorisations, least squares, eigenvalue and singular value problems, and Krylov subspace iterations at the level needed to implement them.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Numerical Analysis
Numerical Recipes
Official companion site to Press, Teukolsky, Vetterling and Flannery's Numerical Recipes, giving online access to the third-edition text plus C++ source for interpolation, linear algebra, integration, ODEs, optimisation and statistical routines.
Nick Higham's Blog
Posts by numerical analyst Nicholas J. Higham of the University of Manchester, including the 'What Is' series of short explainers on matrix concepts, floating-point arithmetic notes, software tips, and advice on mathematical writing.
MIT Numerical Computation Guide
Gilbert Strang's course-and-book page for Computational Science and Engineering, collecting chapter material, MATLAB codes, problem sets and 18.085 lecture links covering finite differences, finite elements, Fourier methods and applied linear algebra.
Computational Science and Engineering I (MIT 18.085)
Applied linear algebra for networks, structures and estimation, followed by equilibrium differential equations, Laplace's equation, boundary-value problems, calculus of variations, Fourier series and the discrete Fourier transform. Includes 50 lecture videos, problem sets and exams with solutions, and programming assignments.
An Introduction to Numerical Analysis
Oxford's standard undergraduate text derives and proves the core algorithms: bisection and Newton iteration, Gaussian elimination, polynomial interpolation, orthogonal polynomials, Gaussian quadrature, initial and boundary value problems for ordinary differential equations, and finite elements, with error and stability analysis throughout.
Numerical Linear Algebra
Trefethen and Bau's forty short lectures on matrix computation, starting from the SVD and QR factorisation and building through conditioning, stability, direct solvers, eigenvalue algorithms and iterative methods such as Arnoldi and conjugate gradients.