Generalized orthogonal decompositions of matrix pencils
by
Eugene V. Dulov
Department of Mathematics and Mechanics, Ulyanovsk State University

A number of practical problems involve approximation a set of matrices (matrix pencil), according to some decomposition principle. In a greater part of this applications it's rank is lower than minimum from row or column dimention. Hence arise a problem to find a some kind of approximation via decomposition into constant and variant matrices. The most suitable are orthogonal decompositions, when constant decomposition multipliers are orthogonal matrices, but the variable (middle) matrix can be either rectangular (a type of singular decomposition), or square (a type of polar decomposition). We develop some methods to calculate this decompositions in sence of least squares method and prove necessory theorems to obtain both full- and low-rank decompositions. A proposed methods can be used in various tasks involving matrix estimation and data smoothing. Some computational aspects can be used in 3D visualisation of surfaces, given by a set of points in 3D space via projections.

Date received: November 30, 1999