An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The algebraic eigenvalue problem
The algebraic eigenvalue problem
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Fundamentals of matrix computations
Fundamentals of matrix computations
Jacobi's method is more accurage than QR
SIAM Journal on Matrix Analysis and Applications
Computing the generalized singular value decomposition
SIAM Journal on Scientific Computing
A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
A Divide-and-Conquer Algorithm for the Bidiagonal SVD
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Unitary Triangularization of a Nonsymmetric Matrix
Journal of the ACM (JACM)
Error Analysis of Direct Methods of Matrix Inversion
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186)
Recommender Systems Research: A Connection-Centric Survey
Journal of Intelligent Information Systems
Fast channel estimation using maximum-length shift-register sequences
International Journal of Wireless and Mobile Computing
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures
ACM Transactions on Mathematical Software (TOMS)
Sparkler: supporting large-scale matrix factorization
Proceedings of the 16th International Conference on Extending Database Technology
An improved parallel singular value algorithm and its implementation for multicore hardware
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
| Hi-index | 0.00 |
A matrix decomposition is a factorization of a matrix into the product of simpler matrices. The introduction of matrix decomposition into numerical linear algebra in the years from 1945 to 1965 revolutionized matrix computations. This article outlines the decompositional approach, comments on its history, and surveys the six most widely used decompositions: the Cholesky decomposition, the pivoted LU decomposition, the QR decomposition, the spectral decomposition, the Schur decomposition, and the singular value decomposition.