A Method of Solution for a Large-sized Least-squares Problem with a Block-diagonal Jacobian

摘要

An efficient method of solution is presented for solving a large-sized least-squares problem with a blockdiagonal Jacobian. The method is based on the QR decomposition accompanied with a technique called sequential accumulation and is able to solve a problem with thousands of unknowns on a personal computer. As a numerical example, the least-squares problem that appears in the numerical analysis of diffraction by a layered dielectric grating is solved. Comparison with a conventional QR method in storage requirement and in computation time shows the effectiveness of the present method.