Numerical linear algebra

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Numerical linear algebra

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

Major sub-topics include
* [[Solution of linear equations: direct methods]]
* [[Solution of linear equations: iterative methods]]
* [[Linear least squares]]
* [[Eigenvalue calculations]]

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]], [[w:QR factorization|QR factorization]], [[w:singular value decomposition|singular value decomposition]], and the [[w:Schur decomposition|Schur decomposition]].  Another common issue is how to deal with large, structured matrices, such as [[w:Sparse matrices|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 [[w:Fast Fourier Transfor|Fast Fourier Transform]]).

Some principles worth keeping in mind:
* [[Keep matrices in factored form]]
* [[Use backward error analysis where possible]]
* [[Exploit sparsity where possible]]

[PREREQUISITES]
Linear algebra.

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Numerical linear algebra

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