The authors describe a numerical procedure for solving problems involving minimization over the rotation group of quadratic forms which arise in connection with problems of computer vision. The algorithm presented is a sequential quadratic programming method which takes advantage of the special structure of the problem constraints. It is demonstrate that the method is globally convergent.>

We present a block Lanczos method for computing the greatest singular values and associated vectors of a large and sparse matrix, say A. Our algorithm does not transform A but accesses it through a user-supplied routine that computes the product AX or A tX for a given matrix X.This paper includes a discussion of the various ways to compute the singular-value decomposition of an upper triangular band matrix, this problem arises as a subproblem to be solved in the block Lanczos procedure.