Mathematical Aspects of Scientific SoftwareJ.R. Rice Since scientific software is the fuel that drives today's computers to solve a vast range of problems, huge efforts are being put into the development of new software, systems and algorithms for scientific problem solving. This book explores how scientific software impacts the structure of mathematics, how it creates new subfields, and how new classes of mathematical problems arise. The focus is on five topics where the impact is currently being felt and where important new challenges exist, namely: the new subfield of parallel and geometric computations, the emergence of symbolic computation systems into "general" use, the potential emergence of new, high-level mathematical systems, and the crucial question of how to measure the performance of mathematical problem solving tools. |
Contents
The Mapping Problem in Parallel Computation | 41 |
Applications of Gröbner Bases in Nonlinear | 59 |
The Bézier Method | 89 |
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algebraic curves algorithm analysis applications approach approximation architecture B-spline basis Bezier BLAS Buchberger coefficients Computer Science Connection Machine curves and surfaces data parallel datatype defined derivatives desingularization determined domain ELLPACK equations example Figure finite element finite element analysis Fortran function geometrical graph grid Gröbner bases Gröbner bases method Houstis Ideal(F implementation implicit input Integer intersection curve iteration linear LINPACK LINPACK Band Lisp MACSYMA mapping problem mathematical matrix memory modules monoid multiplication multiprocessor objects operations package parallel computation parallel programming parameter parametric representation Partitioning performance evaluation piecewise planar curve plane polynomial ideal Prep-P primary decomposition primary ideal problem solving properties pvar quadratic real processor rithms robot scientific software Scratchpad singular point solution solvers space curve Sparse LU PIV Sparse LU Uncomp spline superellipsoids symbolic computing theorem tion transformations variables vector virtual processors X X X