Tricki
a repository of mathematical know-how

Numerical linear algebra

Quick description

Numerical linear algebra is the study of numerical algorithms for operations involving matrices and linear equations.

Major sub-topics include

although other operations, such as solving matrix equations, generalized eigenvalue, and other computations are part of this area.

A common feature of much of the work in numerical linear algebra is the use and importance of factorizations, such as the LU factorization, QR factorization, singular value decomposition, and the Schur decomposition. Another common issue is how to deal with large, structured matrices, such as sparse matrices where the few elements are non-zero, or dense matrices with special structure such as the discrete Fourier transform matrix (which is heavily exploited in the Fast Fourier Transform).

Some principles worth keeping in mind:

Prerequisites

Linear algebra.