The least-squares method for matrices dependent on parameters

Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. ©1997 Plenum Publishing Corporation.