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Scientific computing : an introductory survey
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ISBN: 0070276846 0071153365 Year: 1997 Volume: *3 Publisher: New York St. Louis Auckland McGraw-Hill

A brief introduction to numerical analysis
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ISBN: 0817639160 3764339160 1461264138 0817681361 Year: 1997 Publisher: Boston (Mass.) : Birkhäuser,

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Probably I ought to explain why one more book on numerical methods can be useful. Without any doubt, there are many quite good and excellent books on the subject. But I know definitely that I did not realize this when I was a student. In this book, my first desire was to present those lectures that I wished I would have heard when I was a student. Besides, in spite of the profusion of textbooks, introductory courses, and monographs on numerical methods, some of them are too elementary, some are too difficult, some are far too overwhelmedwith applications, and most of them are too lengthy for those who want to see the whole picture in a short time. I hope that the brevity of the course left me no chance to obscure the beauty and depth of mathematical ideas behind the theory and methods of numerical analysis. I am convincedthat such a book should be very conciseindeed. It should be thoroughly structured, giving information in short sections which, ideally, are a half-page in length. Equally important, the book should not give an impression that nothing is left to work on in this field. Any time it becomes possible to say something about modern development and recent results, I do try to find time and place for this.

Numerical methods and software tools in industrial mathematics.
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ISBN: 081763973X Year: 1997 Publisher: Boston Birkhäuser

Numerica : a modeling language for global optimization
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ISBN: 0262720272 9780262288408 9780262720274 0262288400 0585037965 Year: 1997 Publisher: Cambridge : The Mit Press,

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Many science and engineering applications require the user to find solutions to systems of nonlinear constraints or to optimize a nonlinear function subject to nonlinear constraints. The field of global optimization is the study of methods to find all solutions to systems of nonlinear constraints and all global optima to optimization problems. Numerica is modeling language for global optimization that makes it possible to state nonlinear problems in a form close to the statements traditionally found in textbooks and scientific papers. The constraint-solving algorithm of Numerica is based on a combination of traditional numerical methods such as interval and local methods, and constraint satisfaction techniques.This comprehensive presentation of Numerica describes its design, functions, and implementation. It also discusses how to use Numerica effectively to solve practical problems and reports a number of experimental results.A commercial implementation of Numerica is available from ILOG under the name ILOG Numerica.

Numerical range : the field of values of linear operators and matrices
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ISBN: 038794835X 1461384982 9780387948355 Year: 1997 Publisher: New York (N.Y.): Springer

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The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen­ sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func­ tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu­ nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.

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