Elementary theory & application of numerical analysis - Miller, James E. (James Edward) 1937-; Moursund, David G.; Duris, Charles S. (Mineola, N.Y. Dover Publications, 2011)
Preface To The Revised 2011 Dover Edition -- Solution Of Equations By Fixed Point Iteration -- Introduction -- Example -- Principal Algorithm -- Review of Basic Concepts Principal Theorems -- Newton-Raphson Iteration -- Graphical Analysis -- Error Bounds -- Solution Of Linear Equations And Matrix Computations -- Introduction -- Matrices -- Upper-Triangular Systems -- Reduction of Linear System to Upper Triangular Form -- The Inverse of a Square Matrix -- A Better Algorithm for Inverting a Matrix -- Error Aspects -- Estimation of Computation Times -- Iterative Solution Of Systems Of Equations -- Introduction -- Functions of n Variables -- Iteration for Linear Systems -- Nonlinear Systems of Equations -- Polynominals, Taylor's Series And Interpolation Theory -- Introduction -- Evaluation of a Polynomial -- The Taylor Expansion -- Linear Interpolation -- Lagrange Interpolation -- Iterated Interpolation -- Errors And Floating-Point Arithmetic -- Introduction -- Errors -- Floating-point Arithmetic -- Examples from Newton-Raphson Iteration -- Linear-interpolation Example -- Inversion of an Ill-conditioned Matrix -- Examples from Taylor's Series -- Examples of an Infinite Sum -- Numerical Differentiation And Integration -- Introduction -- Numerical Differentiation -- Numerical Integration -- Formulas for Equally Spaced Points -- Remainder Terms -- Integration over Large Intervals -- Richardson's Extrapolation -- Romberg Integration -- Multiple Integrals -- Introduction To The Numerical Solution Of Ordinary Differential Equations -- Introduction -- Existence Theorems for a Single ODE -- Systems of First-Order Equations -- Euler's Method -- Heun's Method -- Error-analysis Aspects -- Numerical Solution Of Ordinary Differential Equations -- Introduction -- Taylor's-Series Procedures -- Runge-Kutta Methods -- Predictor-Corrector Methods.
Moursund's name appears first on the earlier edition
Includes bibliographical references (pages [312]-313) and index.
Originally published
Keywords: Numerical analysis