LAPACK Users' Guide, 3rd Edition

Introduction to Numerical Computation

This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch, and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to numerical computation. The text begins with the basics like error analysis and computer arithmetic, which gives a very solid ground for the origin and handling of numerical errors. It proceeds further to explain more basic topics related to function evaluation, solutions of nonlinear equations, and interpolation techniques. Next, it describes procedures for improving numerical estimates using differentiation and Richardson extrapolation. This is followed by full details of integration, systems of linear equations, and approximation. Finally, ordinary differential equations complete a thorough course of study that will prepare the reader with both the theory and practice that will serve in carrying out numerical computations.

Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans Bruun Nielsen

383 Pages

Numerical Computation Guide

This book is a technical reference to the floating-point environment supported on SPARCTM and x86 platforms running under the Solaris operating system. The book describes the Floating-Point Environment, the representation and computation of floating point numbers and how the results of arithmetic operations are rounded. The Software and Hardware Support section describes how numerical operations are passed between the hardware and software of the system. The book should be indispensable to anyone seeking an understanding of how numerical computations are executed and optimized on Solaris systems. In particular, it will be an asset worth having in real life for developers and engineers working in the field of numerical algorithms within this particular environment of computing and offers a deep view into performance and accuracy considerations.

Author(s): Sun microsystems

NA Pages

Numerical Methods for Scientific Computing

It gives an explanation of all the different numerical methods of scientific computing. It starts with the basics, which is Root Finding and Orthogonal Functions, solving equations and analyzing functions. Finite Differences and Divided Differences included for the needs in the process of numerical differentiation and interpolation. Interpolation and Curve Fitting are given to outline estimation and modeling. It also includes Z-Transforms and Summation Formulas for signal processing and numerical summation. Quadrature Formulas and Ordinary Differential Equations are explained for integration and the solution of differential equations. Partial Differential Equations, Integral Equations, and Stability and Error Analysis form the advanced topics for numerical methods coverage. Further, Monte Carlo Techniques, Message Passing Interface, and Simulation Modeling are included to point out methods for probabilistic simulations and parallel computing.

Author(s): John Henry Heinbockel

NA Pages

Lectures in Basic Computational Numerical Analysis (PDF 168P)

This lecture series provides comprehensive foundational knowledge in the field of numerical computational analysis. Numerical Linear Algebra covers basic matrix operations and solutions of linear systems. The book further goes into the Solution of Nonlinear Equations that shows methods for solving equations which are not linear in form. Finally, it discusses Approximation Theory, showing how functions and data may be approximated. The lectures also cover Numerical Solution of ODEs and PDEs, giving ways to solve these two basic kinds of equations. This resource is intended for students and professionals looking to gain a solid understanding of basic and applied numerical analysis techniques.

Author(s): J. M. McDonough

168 Pages