Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


Mathematics & Statistics

First Advisor

Dr. Adel Boules

Second Advisor

Dr. Champak Panchal

Third Advisor

Dr. Leonard J. Lipkin


A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most cases. A subroutine library that implements the proposed method is listed. Timings and populations of a range of test problems are given.

Included in

Mathematics Commons