Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, bioinformatics, fluid dynamics, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference and finite element methods.

Common problems in numerical linear algebra include computing the following: LU decomposition, QR decomposition, singular value decomposition, eigenvalues.

References

Leader, Jeffery J. (2004). Numerical Analysis and Scientific Computation. Addison Wesley. ISBN 0-201-73499-0.
Bau III, David; Trefethen, Lloyd N. (1997). Numerical linear algebra. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-361-9.
J. H. Wilkinson and C. Reinsch, "Linear Algebra, volume II of Handbook for Automatic Computation" SIAM Review 14, 658 (1972).
Golub, Gene H.; van Loan, Charles F. (1996), Matrix Computations, 3rd edition, Johns Hopkins University Press, ISBN 978-0-8018-5414-9

Numerical linear algebra

Key concepts	Floating point Numerical stability

Problems	Matrix multiplication (algorithms) Matrix decompositions Linear equations Sparse problems

Hardware	CPU cache TLB Cache-oblivious algorithm SIMD Multiprocessing

Software	BLAS Specialized libraries General purpose software

This article is issued from Wikipedia - version of the 11/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.