This book
covers the following topics: Computers for which LAPACK is Suitable, LAPACK Compared with LINPACK and EISPACK, LAPACK and the BLAS, Availability of LAPACK, Commercial Use of LAPACK, Installation of LAPACK, Documentation for LAPACK, Support for LAPACK
and
Errata in LAPACK.
Author(s): E.
Anderson , Z. Bai , C. Bischof , L. S. Blackford , J. Demmel , J. Dongarra , J.
Du Croz , A. Greenbaum , S. Hammarling , A. McKenney and D. Sorensen
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
The
resource described here is an overview of numerical methods important in the
study of computational science and engineering. The text starts off with
Computing with Matrices and Vectors, foundational elements in many algorithms.
The note moves forward and explains Direct Methods for Linear Systems of
Equations and Direct Methods for Linear Least Squares Problems, important
problem-solving aspects in linear algebra. The Filtering Algorithms for data
processing are reviewed, while Data Interpolation and Data Fitting in 1D discuss
ways of approximating onedimensional data. Approximation of Functions in 1D and
Numerical Quadrature introduce the techniques on function approximation and
integration. It also discusses Iterative Methods for Non-Linear Systems of
Equations and Eigenvalues-a critical topic needed for solving complex systems.
It finally includes Numerical Integration and Structure Preserving Integration,
fundamental to perform numerical calculations with appropriate accuracy in
scientific computing.
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.
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.