Numerical Linear Approximation in C

ISBN-13: 9780367387310 / Angielski / Miękka / 2019 / 968 str.

Nabih Abdelmalek; William A. Malek

Opis

Featuring the C programming language to implement algorithms, this work provides a unique collection of linear approximation techniques that can be used to analyze, model, and compress discrete data in a variety of fields. It focuses on various L₁, Chebyshev, and least squares approximations, including one-sided, bounded variables, and piecewise. The authors also present the solution of underdetermined systems of consistent linear equations that are subject to different constraints on the elements of the unknown solution vector. They compare numerical results of the algorithms, which are accompanied by solved examples, and include a CD-ROM with source code and test drivers.

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.