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
Wikimedia Commons has media related to Numerical linear algebra.
- 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
Further Reading
- Golub, Gene H.; Van Loan, Charles F. (1996). Matrix Computations (3rd ed.). Baltimore: The Johns Hopkins University Press.
- Matrix Iterative Analysis, Varga, Richard S., Springer, 2000.
- Higham, N. J. (2002). Accuracy and stability of numerical algorithms. Society for Industrial and Applied Mathematics.
- Liesen, J., & Strakos, Z. (2012). Krylov subspace methods: principles and analysis. OUP Oxford.
