An Interval Algorithm For Solving Systems Of Linear Equations To Prespecified Accuracy
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Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.
An interval algorithm for solving systems of linear equations to prespecified accuracy
We describe an interval arithmetic algorithm for solving a special class of simulataneous linear equations. This class includes but is not limited to systems Ax=b where A and b have integer entries. The algorithm uses fixed point arithemetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy e desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.