Gradimir V. Milovanovic's Books

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

By: Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanovic

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Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

By: Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanovic

Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions Contains exhaustive references with thousands of citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research

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Page Count

442

Publisher

Elsevier

Published Date

ISBN 10

0128119888

ISBN 13

9780128119884

Topics In Polynomials: Extremal Problems, Inequalities, Zeros

By: Gradimir V Milovanovic,Themistocles M Rassias,D S Mitrinovic

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Topics In Polynomials: Extremal Problems, Inequalities, Zeros

By: Gradimir V Milovanovic,Themistocles M Rassias,D S Mitrinovic

The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.

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Page Count

844

Publisher

World Scientific

Published Date

ISBN 10

9814506486

ISBN 13

9789814506489

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

By: Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanović

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Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

By: Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanović

Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. - Applies Markov-Bernstein-type inequalities to any problem where derivative estimates are necessary - Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions, and entire functions of exponential type - Contains exhaustive references with more than five hundred citations to articles and books - Features methods to solve inverse problems across approximation theory - Includes open problems for further research

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444

Publisher

Academic Press

Published Date

ISBN 10

012812007X

ISBN 13

9780128120071

Interpolation Processes

Basic Theory and Applications

By: Giuseppe Mastroianni,Gradimir Milovanovic

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Interpolation Processes

Basic Theory and Applications

By: Giuseppe Mastroianni,Gradimir Milovanovic

Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.

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Page Count

452

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540683496

ISBN 13

9783540683490

Book's by Gradimir V. Milovanovic

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Topics In Polynomials: Extremal Problems, Inequalities, Zeros

Topics In Polynomials: Extremal Problems, Inequalities, Zeros

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Interpolation Processes

Interpolation Processes

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