Numerical linear algebra

In the field of numerical analysis, numerical linear algebra is an area to study methods to solve problems in linear algebra by numerical computation^[1]^[2]^[3]. The following problems will be considered in this area:

Numerically solving a system of linear equations^[4].
Numerically solving an eigenvalue problem for a given matrix^[5].
Computing approximate values of a matrix-valued function^[6].

Numerical errors can occur in any kind of numerical computation including the area of numerical linear algebra. Errors in numerical linear algebra are considered in another area called "validated numerics"^[7].

References

↑ Demmel, J. W. (1997). Applied numerical linear algebra. SIAM.
↑ Ciarlet, P. G., Miara, B., & Thomas, J. M. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.
↑ Trefethen, Lloyd; Bau III, David (1997). Numerical Linear Algebra (1st ed.). Philadelphia: SIAM.
↑ Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.
↑ David S. Watkins (2008), The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM.
↑ Higham, N. J. (2008). Functions of matrices: theory and computation. SIAM.
↑ Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.

External Links

Freely available software for numerical algebra on the web, composed by Jack Dongarra and Hatem Ltaief, University of Tennessee
NAG Library of numerical linear algebra routines
Numerical Linear Algebra Group on Twitter (Research group in the United Kingdom)
siagla on Twitter (Activity group about numerical linear algebra in the Society for Industrial and Applied Mathematics)
The GAMM Activity Group on Applied and Numerical Linear Algebra

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[1] Demmel, J. W. (1997). Applied numerical linear algebra. SIAM.

[2] Ciarlet, P. G., Miara, B., & Thomas, J. M. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.

[3] Trefethen, Lloyd; Bau III, David (1997). Numerical Linear Algebra (1st ed.). Philadelphia: SIAM.

[4] Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.

[5] David S. Watkins (2008), The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM.

[6] Higham, N. J. (2008). Functions of matrices: theory and computation. SIAM.

[7] Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.

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