Mathematical Software

Mathematical Software III contains the proceedings of the Symposium on Mathematical Software held in Madison, Wisconsin, on March 28-30, 1977, under the auspices of the Mathematics Research Center at the University of Wisconsin-Madison. The papers focus on software designed for mathematical applications such as LINPACK for the solution of linear systems and least squares problems and ELLPACK for elliptic partial differential equations.

Comprised of 14 chapters, this volume begins with an overview of LINPACK, a software package designed to solve linear systems and least squares problems. The reader is then introduced to an extension to the exchange algorithm for solving overdetermined linear equations; infallible calculation of polynomial zeros to specified precision; and representation and approximation of surfaces. Subsequent chapters discuss the ways in which mathematical software and exploratory data analysis should interact to satisfy their respective needs; production of mathematical software; computational aspects of the finite element method; and multi-level adaptive techniques for partial differential equations. The book also describes a realistic model of floating-point computation before concluding with an evaluation of the Block Lanczos method for computing a few of the least or greatest eigenvalues of a sparse symmetric matrix.

This monograph should be of considerable interest to students and specialists in the fields of mathematics and computer science.

Inhalt

Contributors
Preface
Research, Development, and LINPACK
A Technique that Gains Speed and Accuracy in the Minimax Solution of Overdetermined Linear Equations
Infallible Calculation of Polynomial Zeros to Specified Precision
Representation and Approximation of Surfaces
Simulation: Conflicts Between Real-Time and Software
Mathematical Software and Exploratory Data Analysis
Software for C1 Surface Interpolation
Mathematical Software Production
Computational Aspects of the Finite Element Method
The Art of Writing a Runge-Kutta Code, Part I
Multi-Level Adaptive Techniques (MLAT) for Partial Differential Equations: Ideas and Software
ELLPACK: A Research Tool for Elliptic Partial Differential Equations Software
A Realistic Model of Floating-Point Computation
The Block Lanczos Method for Computing Eigenvalues
Index