Study of Solution of a Large System of Linearized Normal Equations and the Inversion of the Associated Coefficient Matrix

摘要

Methods were studied to solve and invert the normalized coefficient matrices generated in analytical triangulation. These matrices are positive definite and each has three or five bands of non-zero entries by blocks. Each block of the matrix can be up to 600 x 600 in size. As a result of the study, block successive over-relaxation (BSOR) techniques were selected and incorporated in a computer program written in the Fortran IV language for the IBM 7094. This program can solve matrices up to 30,000 x 30,000. Besides a discussion of the BSOR techniques and a complete documentation of the computer program, the report describes alternate mathematical techniques. (Author)