Estimates of the Roundoff Error in the Solution of A System of Conditional Equations

摘要

The paper compares the roundoff error in the least-squares solution of a system of conditional equations Ax=f by two different methods, using backward error analysis. The first one entails solving the normal equations (A sup T)Ax = (A sup T)f and the second is one proposed by Faddeev, Faddeeva, and Kublanovskaya in 1966. This latter method involves multiplying the system by othogonal matrices to transform the matrix A into upper triangular form. (Author)