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On solution of total least squares problems with multiple right‐hand sides
Author(s) -
Hnětynková Iveta,
Plešinger Martin,
Strakoš Zdeněk
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810815
Subject(s) - least squares function approximation , mathematics , core (optical fiber) , linear least squares , combinatorics , algorithm , computer science , statistics , telecommunications , estimator , singular value decomposition
Consider a linear approximation problem AX ≈ B with multiple right–hand sides. When errors in the data are confirmed both to B and A , the total least squares (TLS) concept is used to solve this problem. Contrary to the standard least squares approximation problem, a solution of the TLS problem may not exist. For a single (vector) right–hand side, the classical theory has been developed by G.H. Golub, C.F. Van Loan [2], and S. Van Huffel, J. Vandewalle [4], and then complemented recently by the core problem approach of C.C. Paige, Z. Strakoš [5,6,7]. Analysis of the problem with multiple right–hand sides is still under development. In this short contribution we present conditions for the existence of a TLS solution. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)