2.5 Adjustment algorithm with sparse technique

Multiplication, factorisation and inversion of matrices are operations in which the computing effort is a function of the third power of the number of rows or columns. In adjustment computations, however, many matrix elements are zero (especially for large networks). The proportion of non-zero elements is in the most cases less than 5%, sometimes even less than. The coefficient matrix A (see 2.1/1) may even have less than of non-zero elements. In order to reduce storage requirements and computing time, techniques are adopted which (completely or partially) avoid storage of zero elements and computation with zero elements.

In the A matrix, only the non-zero coefficients are stored by rows together with the corresponding column numbers. Optionally as well from the N matrix only the non-zero elements can be stored.

Contrary to , the matrix C is as well merely a sparse matrix, so that all operations can be done by means of sparse-techniques. Matrices are stored by means of the profile storage scheme.