Polynomial Problems
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Nondifferentiable Optimization And Polynomial Problems
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Author : N.Z. Shor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nondifferentiable Optimization And Polynomial Problems written by N.Z. Shor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.
Topics In Polynomials
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Author : G V Milovanovic
language : en
Publisher: World Scientific
Release Date : 1994-06-28
Topics In Polynomials written by G V Milovanovic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-28 with Science categories.
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. Contents:PrefaceGeneral Concept of Algebraic PolynomialsSelected Polynomial InequalitiesZeros of PolynomialsInequalities Connected with Trigonometric SumsExtremal Problems for PolynomialsExtremal Problems of Markov-Bernstein TypeSome Applications of PolynomialsSymbol IndexName IndexSubject Index Readership: Mathematicians and mathematical physicists. keywords:Algebraic Polynomials;Trigonometric Polynomials;Zeros;Extremal Problems;Trigonometric Sums;Positivity and Monotonicity;Distribution of Zeros;Bounds for Polynomial Zeros;Incomplete Polynomials;Polynomials with Minimal Norm;Markov-Bernstein Inequalities;Approximation;Symmetric Functions;Orthogonal Polynomials;Nonnegative Polynomials “The topics are tastefully selected and the results are easy to find. Although this book is not really planned as a textbook to teach from, it is excellent for self-study or seminars. This is a very useful reference book with many results which have not appeared in a book form yet. It is an important addition to the literature.” Journal of Approximation Theory “I find the book to be well written and readable. The authors have made an attempt to present the material in an integrated and self-contained fashion and, in my opinion, they have been greatly successful. The book would be useful not only for the specialist mathematician, but also for those researchers in the applied and computational sciences who use polynomials as a tool.” Mathematical Reviews “This is a remarkable book, offering a cornucopia of results, all connected by their involvement with polynomials. The scope of the volume can be conveyed by citing some statistics: there are 821 pages, 7 chapters, 20 sections, 108 subsections, 95 pages of references (distributed throughout the book), a name index of 16 pages, and a subject index of 19 pages … The book is written in a gentle style: one can open it anywhere and begin to understand, without encountering unfamiliar notation and terminology. It is strongly recommended to individuals and to libraries.” Mathematics of Computation “This book contains some of the most important results on the analysis of polynomials and their derivatives … is intended, not only for the specialist mathematician, but also for those researchers in the applied sciences who use polynomials as a tool.” Sever S Dragomir “This is a well-written book on a widely useful topic. It is strongly recommended not only to the mathematical specialist, but also to all those researchers in the applied and computational sciences who make frequent use of polynomials as a tool. Of course, libraries will also benefit greatly by including this book in their cherished collection.” Mathematics Abstracts “There is no doubt that this is a very useful work compiling enormous researches carried out on the subject … This is a well-written book on a widely useful topic.” Zentralblatt für Mathematik
Polynomial Problems
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Author : Beverly Nance
language : en
Publisher: Milliken Publishing Company
Release Date : 1991-09-01
Polynomial Problems written by Beverly Nance and has been published by Milliken Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-01 with Education categories.
There are certain mistakes that students frequently make while learning algebra. This packet, focusing on polynomials, clearly explains these mistakes so students can avoid them. Examples then illustrate the correct way of working an algebra problem, and practice problems are provided. Puzzles and games based on scientific formulas and interesting facts challenge students to think creatively. Self-checking exercises motivate students to finish each page while acquiring valuable algebraic skills.
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems
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Author : Alexander Morgan
language : en
Publisher: SIAM
Release Date : 2009-01-01
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems written by Alexander Morgan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Computers categories.
This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations. Originally published in 1987, it remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for high-school and undergraduate mathematics projects. Audience: accessible to readers with limited mathematical backgrounds. It is appropriate for undergraduate mechanical engineering courses in which robotics and mechanisms applications are studied.
Polynomial Problems
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Author : Sara Freeman
language : en
Publisher: Milliken Publishing Company
Release Date : 2002-09-01
Polynomial Problems written by Sara Freeman and has been published by Milliken Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-01 with Education categories.
This easy-to-use packet is chock full of stimulating activities that will jumpstart your students' interest in algebra while reinforcing major concepts. A variety of puzzles, games, and worksheets will challenge students as they multiply, divide, and factor polynomials. A special assessment page to help prepare students for standardized tests and an answer key are also included.
Problems And Theorems In Analysis
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Author : Georg Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Problems And Theorems In Analysis written by Georg Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Extremal Problems And Inequalities Of Markov Bernstein Type For Algebraic Polynomials
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Author : Robert B. Gardner
language : en
Publisher: Academic Press
Release Date : 2022-02-10
Extremal Problems And Inequalities Of Markov Bernstein Type For Algebraic Polynomials written by Robert B. Gardner and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
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
Problems And Theorems In Analysis Ii
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Author : George Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-11
Problems And Theorems In Analysis Ii written by George Polya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.
Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.
Numerical Polynomial Algebra
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Author : Hans J. Stetter
language : en
Publisher: SIAM
Release Date : 2004-01-01
Numerical Polynomial Algebra written by Hans J. Stetter and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.
Polynomials
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Author : E.J. Barbeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Polynomials written by E.J. Barbeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.
The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.