Numerical Computation 1: Methods, Software, and AnalysisSpringer Science & Business Media, 2012 M12 6 - 474 pages This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous. |
Contents
1 | |
9 | |
3 | 23 |
4 | 37 |
5 | 46 |
Computers for Numerical Data Processing | 68 |
3 | 90 |
1 | 106 |
37 | 261 |
1 | 272 |
3 | 280 |
4 | 295 |
1 | 308 |
The Homogenization of Discrete Data | 316 |
Constraints | 335 |
7 | 350 |
14 | 138 |
21 | 144 |
Numerical Algorithms | 172 |
28 | 197 |
29 | 216 |
Numerical Programs | 219 |
6 | 249 |
34 | 254 |
7 | 258 |
Interpolation | 353 |
39 | 382 |
42 | 389 |
48 | 398 |
54 | 408 |
Glossary of Notation | 440 |
Author Index | 460 |
Other editions - View all
Numerical Computation 1: Methods, Software, and Analysis Christoph W. Ueberhuber Limited preview - 1997 |
Common terms and phrases
accuracy algebraic approximating function arithmetic operations B-splines binary cache calculated Chebyshev Chebyshev nodes Chebyshev polynomials coefficients complexity computational effort computer systems condition number cubic spline data points defined degree denormalized depends derivative determined differential digits discrete efficiency END DO END evaluation Example execution exponent finite floating-point number system floating-point operations floating-point performance Fortran 90 function f function values hardware IEC/IEEE implementation increase instructions integration intermediate results Internet interpolation function interpolation nodes interpolation polynomial interval LAPACK linear equations LINPACK locality of reference loop unrolling main memory mantissa mathematical matrix matrix-matrix multiplication memory hierarchy method Mflop/s NETLIB norm numerical data processing numerical software obtained operands optimal parameters perturbations piecewise pipeline polynomial interpolation possible precision processor programming languages real numbers representation rounding error Section sequence solution solve specified Strassen algorithm subroutine summation system of linear theorem transformations variant vector vector processors workstation zero