文档介绍：General Preface
In the early eighties, when Jacques-Louis Lions and I considered the idea of a Hand-
book of Numerical Analysis, we carefully laid out specific objectives, outlined in the
following excerpts from the “General Preface” which has appeared at the beginning of
each of the volumes published so far:
During the past decades, giant needs for ever more sophisticated mathe-
matical models and plex and puter simula-
tions have arisen. In this fashion, two indissociable activities, mathematical
modeling puter simulation, have gained a major status in all aspects
of science, technology and industry.
In order that these two sciences be established on the safest possible
grounds, mathematical rigor is indispensable. For this reason, pan-
ion sciences, Numerical Analysis and Scientific Software, have emerged as
essential steps for validating the mathematical models and puter
simulations that are based on them.
Numerical Analysis is here understood as the part of Mathematics that de-
scribes and analyzes all the numerical schemes that are used puters;
its objective consists in obtaining a clear, precise, and faithful, representa-
tion of all the “information” contained in a mathematical model; as such, it
is the natural extension of more classical tools, such as analytic solutions,
special transforms, functional analysis, as well as stability and asymptotic
analysis.
The various prising the Handbook of Numerical Analysis
will thoroughly cover all the major aspects of Numerical Analysis, by pre-
senting accessible and in-depth surveys, which include the most recent
trends.
More precisely, the Handbook will cover the basic methods of Numerical
Analysis, gathered under the following general headings:
– Solution of Equations in Rn,
– Finite Difference Methods,
– Finite Element Methods,
– Techniques of puting.
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vi General Preface
It will also cover the numerical solution of actual problems of contempo-
rary i