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

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.

Keywords

• linear approximation problem
• total least squares
• multiple right-hand sides
• core problem