Interval Analysis

5.4Direct methods

The interval Gaussian algorithm – basics

In numerical analysis the Gaussian algorithm is a popular method for solving linear systems of equations Ax = b with regular, nonstructured and moderately-sized matrices A. Although we assume that the reader is familiar with the Gaussian algorithm, we repeat the essential ideas in order to apply them to interval linear systems later on. We first describe the algorithm in its standard form, i.e., without interchanging rows or columns. We start with a linear system in matrix-vector form

in which we will eliminate the variable x₁ in all equations except the first one. To this end we multiply ...