Block decomposition algorithms for matrices in dual angular form

^min⁄_x | | b - Ax | |₂

where A is a real m x n matrix of rank n , are presented. The observation matrix A is assumed to be in dual angular form:

A =

Such matrices arise, for example, in geodetic adjustments and in mathematical programming.

Two block decomposition algorithms, one using block Cholesky decomposition and the other using block orthogonal decomposition by Householder transformations are given. Applications to geodetic adjustments are discussed in detail. Computer implementations of the two algorithms are compared in terms of their numerical efficiencies. A FORTRAN program for each algorithm is provided along with some numerical examples. The block Householder algorithm was found to be faster, more accurate, and take less storage than the block Cholesky algorithm in most of the test examples given.