Explores spectral methods built around MATLAB programmes. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of ......
This updated version of "Solving Linear Systems on Vector and Shared Memory Computers" (SIAM, 1990) discusses major elements of the new advanced-architecture computers and recent developments in the solution of systems of linear equations and eigenvalue algorithms for dense and sparse matrices that are designed to exploit these elements. It ......
Computational Integration is the first book in over 10 years dedicated to a comprehensive discussion of computational integration methods and the fundamental mathematical principles they are based on. It gives special coverage of many recent developments, such as parallel integration algorithms, that have not yet been coherently presented in any ......
In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and ......
Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in ......
Devoted to the assessment of the quality of numerical results produced by computers, this book addresses the question, how does finite precision affect the convergence of numerical methods on the computer when convergence has been proven in exact arithmetic? Finite precision computations are at the heart of the activities of many engineers and ......
A reprint of the original volume, which won the Lanchester Prize awarded by the Operations Research Society of America for the best work of 1968. Although out of print for nearly 15 years, it remains one of the most referenced volumes in the field of mathematical programming. Recent interest in interior point methods generated by Karmarkar's ......
Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms. Results that lead to applications in the area of signal processing are emphasized, ......
This monograph deals with aspects of the computer programming process that involve techniques derived from mathematical logic. The author focuses on proving that a given program produces the intended result whenever it halts, that a given program will eventually halt, that a given program is partially correct and terminates, and that a system of ......
