Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
Abstract: In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw