The core problem within a linear approximation problem with multiple right-hand sides

• ID: 2677, RIV: 10285107
• ISSN: not specified, ISBN: 978-80-87136-16-4
• source: SNA´14 - Seminar on Numerical Analysis: Modelling and Simulation of Challenging Engineering Problems
• keywords: linear approximation problem; total least squares; multiple right-hand sides; core problem
• authors: Iveta Hnětynková, Martin Plešinger, Diana M. Sima, Zdeněk Strakoš, Sabina Van Huffel
• authors from KNM: Strakoš Zdeněk, Hnětynková Iveta

Abstract

In total least squares (TLS) formulation of a linear approximation problem AX ~ B with multiple right-hand sides, we seek a minimal correction to B and A giving a compatible problem. It is well known that even in the single right-hand side case the TLS problem may not have a solution and when the solution exists, it may not be unique. Problems with d = 1 have been revisited by Ch. Paige and Z. Strakoš introducing the so called core theory. In this presentation, we study the existence and uniqueness of a TLS solution with d > 1. We present a generalization of the core theory to the multiple right-hand side case.