Bidiagonalization of Matrices and Solution of Linear Equations.

摘要

An algorithm given by Golub and Kahan for reducing a general matrix to bidiagonal form is shown to be very important for large sparse matrices. The singular values of the matrix are those of the bidiagonal form,and these can be easily computed. The bidiagonalization algorithm is shown to be the basis of important methods for solving the linear least squares problem for large sparse matrices. Eigenvalues of certain 2-cyclic matrices can also be efficiently computed using this bidiagonalization. (Author)