SOME APPLICATIONS OF THE RANK REVEALING QR FACTORIZATION
- 30 April 1992
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific and Statistical Computing
- Vol. 13 (3), 727-741
- https://doi.org/10.1137/0913043
Abstract
The rank revealing QR factorization of a rectangular matrix can sometimes be used as a reliable and efficient computational alternative to the singular value decomposition for problems that involve rank determination. This is illustrated by showing how the rank revealing QR factorization can be used to compute solutions to rank deficient least squares problems, to perform subset selection, to compute matrix approximations of given rank, and to solve total least squares problems.This publication has 18 references indexed in Scilit:
- On updating signal subspacesIEEE Transactions on Signal Processing, 1992
- Computing Truncated Singular Value Decomposition Least Squares Solutions by Rank Revealing QR-FactorizationsSIAM Journal on Scientific and Statistical Computing, 1990
- Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical RankSIAM Journal on Scientific and Statistical Computing, 1990
- Least squares methodsPublished by Elsevier BV ,1990
- Tracking a few extreme singular values and vectors in signal processingProceedings of the IEEE, 1990
- The truncatedSVD as a method for regularizationBIT Numerical Mathematics, 1987
- Rank revealing QR factorizationsLinear Algebra and its Applications, 1987
- Rank and null space calculations using matrix decomposition without column interchangesLinear Algebra and its Applications, 1986
- An Improved Algorithm for Computing the Singular Value DecompositionACM Transactions on Mathematical Software, 1982
- Linear least squares solutions by householder transformationsNumerische Mathematik, 1965