numerical linear approximation in c

ISBN-13: 9781584889786 / Angielski / Twarda / 2008 / 962 str.

Nabih Abdelmalek; William A. Malek

Opis

Illustrating the relevance of linear approximation in a variety of fields, Numerical Linear Approximation in C presents a unique collection of linear approximation algorithms that can be used to analyze, model, and compress discrete data. Developed by the lead author, the algorithms have been successfully applied to several engineering projects at the National Research Council of Canada. Basing most of the algorithms on linear programming techniques, the book begins with an introductory section that covers applications, the simplex method, and matrices. The next three parts focus on various L₁, Chebyshev, and least squares approximations, including one-sided, bounded variables, and piecewise. The final section presents the solution of underdetermined systems of consistent linear equations that are subject to different constraints on the elements of the unknown solution vector. Except in the preliminary section, all chapters include the C functions of the algorithms, along with drivers that contain numerous test case examples and results. The accompanying CD-ROM also provides the algorithms written in C code as well as the test drivers. To use the software, it is not required to understand the theory behind each function.

Spis treści

Applications of Linear Approximation. Preliminaries. Linear Programming and the Simplex Algorithm.Efficient Solutions of Linear Equations.Linear L₁ Approximation.One-Sided L₁ Approximation.L₁ Approximation with Bounded Variables.L₁ Polygonal Approximation of Plane Curves.Piecewise L₁ Approximation of Plane Curves. Linear Chebyshev Approximation.One-Sided Chebyshev Approximation.Chebyshev Approximation with Bounded Variables.Restricted Chebyshev Approximation.Strict Chebyshev Approximation.Piecewise Chebyshev Approximation.Solution of Linear Inequalities.Least Squares and Pseudo-Inverses of Matrices.Piecewise Linear Least Squares Approximation.Solution of Ill-Posed Linear Systems.L₁ Solution of Underdetermined Linear Equations.Bounded and L₁ Bounded Solutions of Underdetermined Linear Equations.Chebyshev Solution of Underdetermined Linear Equations. Bounded Least Squares Solution of Underdetermined Linear Equations. Appendices. Index.

O autorze

Abdelmalek, Nabih; Malek, William A.