Gisela Engeln-Müllges

Numerical algorithms with C

More scientists now use C than any other programming language. This book contains practical, computer-ready algorithms for many standard methods of numerical mathematics. It describes the principles of the various methods and provides support in choosing the appropriate method for a given task. Topics given special emphasis include converging methods for solving nonlinear equations, methods for solving systems of linear equations for many special matrix structures, and the Shepard method for multidimensional interpolation. The CD contains C-programs for almost all the algorithms given in the book and a compiler, together with software for graphical printing.

Numerical algorithms with Fortran

This is a completely up-to-date compendium of Fortran algorithms for numerical mathematics, including many sophisticated algorithms which are not available elsewhere. All have been extensively field-tested and cover methods for solving nonlinear equations, the method of Laguerre for solving algebraic equations, conjugating gradients for solving linear systems of equations, and the McKee algorithm for solving special systems of symmetric equations. The real, practical algorithms provided make the book indispensable for applied scientists working in all areas of research. The CD contains Fortran programs for the algorithms given in the text.

Die endliche Fourier- und Walsh-Transformation mit einer Einführung in die Bildverarbeitung

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Systems of Nonlinear Equations

This chapter extends chapter 2 from solving one nonlinear equation in one unknown to systems of nonlinear equations. Assume that we are given a system of n nonlinear equations for an ( n in mathbb{N} ) with n ≥ 2: n n

Akima- und Renner-Subsplines

begin{cases} f_1 (x_1 ,x_2 , ldots ,x_n ) = 0, hfill f_2 (x_1 ,x_2 , ldots ,x_n ) = 0, hfill vdots ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, vdots hfill f_n (x_1 ,x_2 , ldots ,x_n ) = 0. hfill end{cases}

Direkte Verfahren zur Lösung linearer Gleichungssysteme

n n(6.1)

Numerische Verfahren zur Lösung nichtlinearer Gleichungen

If f is a real-valued function defined on a closed interval I = [a, b], then a number ξ ∈ I is called a zero or a root of the function f, or a solution of the equation n n