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The book of Professor Evtushenko describes both the theoretical
foundations and the range of applications of many important methods
for solving nonlinear programs. Particularly emphasized is their
use for the solution of optimal control problems for ordinary
differential equations. These methods were instrumented in a
library of programs for an interactive system (DISO) at the
Computing Center of the USSR Academy of Sciences, which can be used
to solve a given complicated problem by a combination of
appropriate methods in the interactive mode. Many examples show the
strong as well the weak points of particular methods and illustrate
the advantages gained by their combination. In fact, it is the
central aim of the author to pOint out the necessity of using many
techniques interactively, in order to solve more dif ficult
problems. A noteworthy feature of the book for the Western reader
is the frequently unorthodox analysis of many known methods in the
great tradition of Russian mathematics. J. Stoer PREFACE
Optimization methods are finding ever broader application in sci
ence and engineering. Design engineers, automation and control
systems specialists, physicists processing experimental data, eco
nomists, as well as operations research specialists are beginning
to employ them routinely in their work. The applications have in
turn furthered vigorous development of computational techniques and
engendered new directions of research. Practical implementa tion of
many numerical methods of high computational complexity is now
possible with the availability of high-speed large-memory digital
computers."
New edition of a well-known classic in the field; Previous edition
sold over 6000 copies worldwide; Fully-worked examples; Many
carefully selected problems
This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: fully worked-out examples; many carefully selected and formulated problems; fast Fourier transform methods; a thorough discussion of some important minimization methods; solution of stiff or implicit ordinary differential equations and of differential algebraic systems; modern shooting techniques for solving two-point boundary value problems; and basics of multigrid methods. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. New material on differential equations and the iterative solution of linear equations include: solving differential equations in the presence of discontinuities whose locations are not known at the outset; techniques for sensitivity analyses of differential equations dependent on additional parameters; new advanced techniques in multiple shooting; and Krylov space methods for non-symmetric systems of linear equations.
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