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Monte Carlo and Quasi-Monte Carlo methods 1996 1

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丛书名： Lecture Notes in Statistics

1000年

作者： Harald Niederreiter Peter Hellekalek Gerhard Larcher Peter Zinterhof

ISBN: (数字)9781461216902

ISBN: (纸本)9780387983356

Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International conference on Monte Carlo and Quasi-Monte Carlo methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.

关键词： applications of Mathematics

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RIGOROUS numerical ANALYSIS WITH HIGH-ORDER TAYLOR MODELS

RIGOROUS NUMERICAL ANALYSIS WITH HIGH-ORDER TAYLOR MODELS

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作者： Jens Hoefkens Michigan State University

学位级别：博士

Interval techniques have been utilized for rigorous numerical analysis since the 1960s. However, their use has been limited by the dimensionality curse and the dependency problem. The recently developed Taylor model approach alleviates these problems and allows the use of validated numerics in a wide range of applications. To broaden the applicability of the Taylor model method, we introduce new algorithms for the inversion of functional relations and the integration of differential algebraic equations. First we present a new method for computing veri ed enclosures of the inverses of given functions over large domains. The approach utilizes Taylor models and the sharpness of the enclosures scales with a high order of the domain. An integral part of the new method is the rigorous determination of invertibility of high dimensional functions over large domains, which is reduced to a veri ed linear algebra problem in- volving only first derivatives of the function of interest. Several examples highlighting various aspects of the methods are discussed. Differential algebraic equations (DAES) describe important problems in mechani- cal and chemical engineering. Existing algorithms for the integration of DAE initial value problems have traditionally been restricted to low-index systems and until re- cently, no practical scheme for the veri ed integration of DAEs existed. Recognizing the antiderivation as a natural operation on Taylor models yields a method that treats DAEs within a fully differential algebraic context as implicit equations made of con- ventional functions and the antiderivation. The resulting integration scheme can be applied to high-index problems and allows the computation of guaranteed enclosures of nal coordinates from large initial regions. To demonstrate the general applicability of the Taylor model approach, we present results from veri ed asteroid orbit integrations and the theory of Hamiltonian systems. We show that the newly developed methods are

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Applied Parallel and Scientific Computing 1

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丛书名： Lecture Notes in Computer Science

1000年

ISBN: (数字)9783642281457

ISBN: (纸本)9783642281440

The two volume set LNCS 7133 and LNCS 7134 constitutes the thoroughly refereed post-conference proceedings of the 10th International conference on Applied Parallel and Scientific Computing, PARA 2010, held in Reykjavík, Iceland, in June 2010. These volumes contain three keynote lectures, 29 revised papers and 45 minisymposia presentations arranged on the following topics: cloud computing, HPC algorithms, HPC programming tools, HPC in meteorology, parallel numerical algorithms, parallel computing in physics, scientific computing tools, HPC software engineering, simulations of atomic scale systems, tools and environments for accelerator based computational biomedicine, GPU computing, high performance computing interval methods, real-time access and processing of large data sets, linear algebra algorithms and software for multicore and hybrid architectures in honor of Fred Gustavson on his 75th birthday, memory and multicore issues in scientific computing - theory and praxis, multicore algorithms and implementations for application problems, fast PDE solvers and a posteriori error estimates, and scalable tools for high performance computing.

关键词： Mathematics of Computing Software Engineering/Programming and Operating Systems Algorithm Analysis and Problem Complexity Complexity Computational Mathematics and numerical Analysis Computer Communication Networks

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numerical Fourier Analysis 2

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丛书名： Applied and numerical Harmonic Analysis

1000年

作者： Gerlind Plonka Daniel Potts Gabriele Steidl Manfred Tasche

ISBN: (数字)9783031350054

ISBN: (纸本)9783031350047;9783031350078

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis.;The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions.;This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others.;will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

关键词： Fourier Analysis Abstract Harmonic Analysis numerical Analysis Mathematical applications in Computer Science linear algebra

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Lectures in Abstract algebra 1

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丛书名： Graduate Texts in Mathematics

1000年

作者： Nathan Jacobson

ISBN: (数字)9781468470536

ISBN: (纸本)9781468470550

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presupposed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essentialtools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

关键词： linear and Multilinear algebras, Matrix theory

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linear algebra, Markov Chains, and Queueing Models 1

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丛书名： The IMA Volumes in Mathematics and its applications

1000年

作者： Carl D. Meyer Robert J. Plemmons

ISBN: (数字)9781461383512

ISBN: (纸本)9781461383536

This IMA Volume in Mathematics and its applications linear algebra, MARKOV CHAINS, AND QUEUEING MODELS is based on the proceedings of a workshop which was an integral part of the 1991-92 IMA program on "Applied linear algebra". We thank Carl Meyer and R.J. Plemmons for editing the proceedings. We also take this opportunity to thank the National Science Founda tion, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. xi PREFACE This volume contains some of the lectures given at the workshop Lin ear algebra, Markov Chains, and Queueing Models held January 13-17, 1992, as part of the Year of Applied linear algebra at the Institute for Mathematics and its applications. Markov chains and queueing models play an increasingly important role in the understanding of complex systems such as computer, communi cation, and transportation systems. linear algebra is an indispensable tool in such research, and this volume collects a selection of important papers in this area. The articles contained herein are representative of the underlying purpose of the workshop, which was to bring together practitioners and re searchers from the areas of linear algebra, numerical analysis, and queueing theory who share a common interest of analyzing and solving finite state Markov chains. The papers in this volume are grouped into three major categories-perturbation theory and error analysis, iterative methods, and applications regarding queueing models.

关键词： linear and Multilinear algebras, Matrix theory

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Foundations of Computational Mathematics 1

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1000年

作者： Felipe Cucker Michael Shub

ISBN: (数字)9783642605390

ISBN: (纸本)9783540616474

This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics conference held at IMPA in Rio de Janeiro in January 1997. Some ofthe others are published in the December 1996 issue of the Journal of Complexity. Both of these publications were available and distributed at the meeting. Even in this aspect we hope to have achieved a synthesis of the mathematics and computer science cultures as well as of the disciplines. The reaction to the Park City meeting on Mathematics of numerical Analy sis: Real Number Algorithms which was chaired by Steve Smale and had around 275 participants, was very enthusiastic. At the suggestion of Narendra Karmar mar a lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale decided to try to hold a periodic meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting. This is then the first edition of FoCM as such. It has been organized around a small collection of workshops, namely - Systems of algebraic equations and computational algebraic geometry - Homotopy methods and real machines - Information-based complexity - numerical linear algebra - Approximation and PDEs - Optimization - Differential equations and dynamical systems - Relations to computer science - Vision and related computational tools There were also twelve plenary speakers.

关键词： algebra Number theory Geometry Algorithm Analysis and Problem Complexity Topology Analysis

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Stochastic Partial Differential Equations and Their applications 1

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丛书名： Lecture Notes in Control and Information Sciences

1000年

ISBN: (数字)9783540470151

ISBN: (纸本)9783540552925

This volume consists of 24 papers submitted for publication by the invited speakers of the IFIP International conference on Stochastic Partial Differential Equations and their Ap- plications. Most of them are research papers, however, a few surveys written by world renowed experts are also included. The aim of the conference was to bring together mathematici- ans, physicists and engineers representing academic as well as industrial fields, interested in the theory and applica- tions of SPDE's. The field of SPDE's is one of the most dy- namically developing areas at the cross roads of several sciences. It is especially attractive for many because of its interdisciplinary character and enormous richness ofal- ready existing as well as potential applications. There were about one hundred participants registered for the conferen- ce. With rare exceptions, all of the most active researchers in the field of SPDE's throughout the world were present at the conference. The main topics for discussion at the confe- rence were: non-linear SPDE's and Markov property for random fields, modern stochastic calculuses, numerical and asympto- tic methods for SPDE's, applications of SPDE's with emphasis onnon-linear filtering, stochastic control and statistical fluid dynamics.

关键词： Control, Robotics, Mechatronics Systems theory, Control Calculus of Variations and Optimal Control Optimization

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numerical Analysis and Its applications 1

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丛书名： Lecture Notes in Computer Science

1000年

作者： Svetozar Margenov Lubin G. Vulkov Jerzy Waśniewski

ISBN: (数字)9783642004643

ISBN: (纸本)9783642004636

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International conference on numerical Analysis and Its applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.

关键词： Programming Techniques Simulation and Modeling numerical Analysis Numeric Computing Algorithm Analysis and Problem Complexity Discrete Mathematics in Computer Science

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applications and Computation of Orthogonal Polynomials 1

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丛书名： International Series of numerical Mathematics

1000年

作者： Walter Gautschi Gerhard Opfer Gene H. Golub

ISBN: (数字)9783034886857

ISBN: (纸本)9783764361372;9783034897280

The workshop on applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.

关键词： Mathematical and Computational Engineering Analysis applications of Mathematics

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