Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems

Authors:
Leslie Foster;Rajesh Kommu
Affiliations:
San Jose State University, San Jose, CA;San Jose State University, San Jose, CA
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2006

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Abstract

Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn2) operations to solve min ‖b − Ax‖ where A is an m by n matrix. We present a modification of the LAPACK routine xGELSY that requires O(mnk) operations where k is the effective numerical rank of the matrix A. For low rank matrices the modification is an order of magnitude faster than the LAPACK code.