Gisela Engeln-Müllges, Frank Uhlig

Numerical Algorithms with Fortran

Übersetzung:Schon, M.; Uhlig, F.

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer, Berlin
• Softcover reprint of the original 1st ed. 1996
• Seitenzahl: 628
• Erscheinungstermin: 13. April 2014
• Englisch
• Abmessung: 235mm x 155mm x 34mm
• Gewicht: 949g
• ISBN-13: 9783642800450
• ISBN-10: 3642800459
• Artikelnr.: 40772972

Autorenporträt

The book has a twofold purpose: for one it provides an easy access to widely tested computer codes for over 130 numerical algorithms. At the same time it gives an informal introduction to the mathematical and computational principles of the underlying methods, as well as practical guidelines for their usage.

Inhaltsangabe

1 Computer Numbers, Error Analysis, Conditioning, Stability of Algorithms and Operations Count.- 1.1 Definition of Errors.- 1.2 Decimal Representation of Numbers.- 1.3 Sources of Errors.- 1.3.1 Input Errors.- 1.3.2 Procedural Errors.- 1.3.3 Error Propagation and the Condition of a Problem.- 1.3.4 The Computational Error and Numerical Stability of an Algorithm.- 1.4 Operations Count, et cetera.- 2 Nonlinear Equations in One Variable.- 2.1 Introduction.- 2.2 Definitions and Theorems on Roots.- 2.3 General Iteration Procedures.- 2.3.1 How to Construct an Iterative Process.- 2.3.2 Existence and Uniqueness of Solutions.- 2.3.3 Convergence and Error Estimates of Iterative Procedures.- 2.3.4 Practical Implementation.- 2.4 Order of Convergence of an Iterative Procedure.- 2.4.1 Definitions and Theorems.- 2.4.2 Determining the Order of Convergence Experimentally.- 2.5 Newton s Method.- 2.5.1 Finding Simple Roots.- 2.5.2 A Damped Version of Newton s Method.- 2.5.3 Newton s Method for Multiple Zeros; a Modified Newton s Method.- 2.6 Regula Falsi.- 2.6.1 Regula Falsi for Simple Roots.- 2.6.2 Modified Regula Falsi for Multiple Zeros.- 2.6.3 Simplest Version of the Regula Falsi.- 2.7 Steffensen Method.- 2.7.1 Steffensen Method for Simple Zeros.- 2.7.2 Modified Steffensen Method for Multiple Zeros.- 2.8 Inclusion Methods.- 2.8.1 Bisection Method.- 2.8.2 Pegasus Method.- 2.8.3 Anderson-Bjorck Method.- 2.8.4 The King and the Anderson-Bjorck-King Methods, the Illinois Method.- 2.8.5 Zeroin Method.- 2.9 Efficiency of the Methods and Aids for Decision Making.- 3 Roots of Polynomials.- 3.1 Preliminary Remarks.- 3.2 The Horner Scheme.- 3.2.1 First Level Horner Scheme for Real Arguments.- 3.2.2 First Level Horner Scheme for Complex Arguments.- 3.2.3 Complete Horner Scheme for Real Arguments.- 3.2.4 Applications.- 3.3 Methods for Finding all Solutions of Algebraic Equations.- 3.3.1 Preliminaries.- 3.3.2 Muller s Method.- 3.3.3 Bauhuber s Method.- 3.3.4 The Jenkins-Traub Method.- 3.3.5 The Laguerre Method.- 3.4 Hints for Choosing a Method.- 4 Direct Methods for Solving Systems of Linear Equations..- 4.1 The Problem.- 4.2 Definitions and Theoretical Background.- 4.3 Solvability Conditions for Systems of Linear Equations.- 4.4 The Factorization Principle.- 4.5 Gaufi Algorithm.- 4.5.1 Gaufi Algorithm with Column Pivot Search.- 4.5.2 Pivot Strategies.- 4.5.3 Computer Implementation of Gaufi Algorithm.- 4.5.4 Gaufi Algorithm for Systems with Several Right Hand Sides.- 4.6 Matrix Inversion via Gaufi Algorithm.- 4.7 Linear Equations with Symmetric Strongly Nonsingular System Matrices.- 4.7.1 The Cholesky Decomposition.- 4.7.2 The Conjugate Gradient Method.- 4.8 The Gaufi Jordan Method.- 4.9 The Matrix Inverse via Exchange Steps.- 4.10 Linear Systems with Tridiagonal Matrices.- 4.10.1 Systems with Tridiagonal Matrices.- 4.10.2 Systems with Tridiagonal Symmetric Strongly Nonsingular Matrices.- 4.11 Linear Systems with Cyclically Tridiagonal Matrices.- 4.11.1 Systems with a Cyclically Tridiagonal Matrix.- 4.11.2 Systems with Symmetric Cyclically Tridiagonal Strongly Nonsingular Matrices.- 4.12 Linear Systems with Five-Diagonal Matrices.- 4.12.1 Systems with Five-Diagonal Matrices.- 4.12.2 Systems with Five-Diagonal Symmetric Matrices.- 4.13 Linear Systems with Band Matrices.- 4.14 Solving Linear Systems via Householder Transformations.- 4.15 Errors, Conditioning and Iterative Refinement.- 4.15.1 Errors and the Condition Number.- 4.15.2 Condition Estimates.- 4.15.3 Improving the Condition Number.- 4.15.4 Iterative Refinement.- 4.16 Systems of Equations with Block Matrices.- 4.16.1 Preliminary Remarks.- 4.16.2 Gaufi Algorithm for Block Matrices.- 4.16.3 Gaufi Algorithm for Block Tridiagonal Systems.- 4.16.4 Other Block Methods.- 4.17 The Algorithm of Cuthill-McKee for Sparse Symmetric Matrices.- 4.18 Recommendations for Selecting a Method.- 5 Iterative Methods for Linear Systems.- 5.1 Preliminary Remarks.- 5.2 Vector and Matrix Norms.- 5.3 The Jacobi Method.-