Core Problem within Linear Approximation
نویسندگان
چکیده
Abstract. This paper focuses on total least squares (TLS) problems AX ≈ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková, M. Plešinger, D. M. Sima, Z. Strakoš, and S. Van Huffel (2011)]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš (2006)] showed how a necessary and sufficient information for solving Ax ≈ b can be revealed from the original data through the so-called core problem concept. In this paper we present an extension of this concept to problems with multiple right-hand sides. The presented data reduction is based on the singular value decomposition of the system matrix A. We show minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side. Some other properties of the the core problem, however, can not be extended for the multiple right-hand sides.
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