En -[Francis_Scheid] Schaum's Outline of Numerical Ana

Preface

The main goal of numerical analysis remains what it has always been, to find

approximate solutions to complex problems using only the simplest operations of

arithmetic. In short, it is a business of solving hard problems by doing lots of easy

steps. Rather clearly, this means finding procedures by which computers can do

the solving for us. The problems come from a variety of mathematical origins,

particularly algebra and analysis, the boundaries being at times somewhat

indistinct. Much background theory is borrowed from such fields by the numerical

analyst, and some must be included in an introductory text for clarity. It is also

true that our subject returns more than raw numbers across the boundaries.

Numerical method has made important contributions to algebraic and analytic

theory.

Many new topics have been added for this second edition. Included are

backward error analysis, splines, adaptive integration, fast Fourier transforms,

finite elements, stiff differential equations, and the QR method. The chapter on

linear systems has been completely rewritten. A number of older topics have

been shortened or eliminated, but a representative portion of classical numerical

analysis has been retained partly for historical reasons. Some of the cuts have

brought a tear to the author's eye, especially that of the constructive proof for the

existence of solutions to differential equations. On the whole the new edition is a

bit more demanding, but the same can be said of the subject itself.

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