Numerical Algorithms with Fortran [Paperback]

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.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 Newtons Method.- 2.5.1 Finding Simple Roots.- 2.5.2 A Damped Version of Newtons Method.- 2.5.3 Newtons Method for Multiple Zeros; a Modified Newtons 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.-l%