Cubature Formulas Modern Analysis
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| Author | : Igor Sobolev |
| Publisher | : CRC Press |
| Total Pages | : 404 |
| Release | : 1993-04-15 |
| Genre | : Science |
| ISBN | : 9782881248412 |
Translated from the Russian revised and updated 1988 edition. Cubature formulas, for calculating the volumes of bodies in multidimensional space, were named by analogy with quadrature formulas, used to calculate the areas of plane figures. Topics include basic concepts and formulations, the polyharmonic equation, simple problems of the theory of computations, order of convergence of cubature formulas, considering a regular boundary layer, optimal formulas, and formulas for rational polyhedra. Annotation copyright by Book News, Inc., Portland, OR
| Author | : S.L. Sobolev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 427 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401589135 |
This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree. These formulas are intended to approximate the calculation of multiple and conventional integrals over a bounded domain of integration. The latter is assumed to have a piecewise-smooth boundary and to be arbitrary in other aspects. Particular emphasis is placed on invariant cubature formulas and those for a cube, a simplex, and other polyhedra. Here, the techniques of functional analysis and partial differential equations are applied to the classical problem of numerical integration, to establish many important and deep analytical properties of cubature formulas. The prerequisites of the theory of many-dimensional discrete function spaces and the theory of finite differences are concisely presented. Special attention is paid to constructing and studying the optimal cubature formulas in Sobolev spaces. As an asymptotically optimal sequence of cubature formulas, a many-dimensional abstraction of the Gregory quadrature is indicated. Audience: This book is intended for researchers having a basic knowledge of functional analysis who are interested in the applications of modern theoretical methods to numerical mathematics.
| Author | : S. L. Sobolev |
| Publisher | : |
| Total Pages | : |
| Release | : 1992 |
| Genre | : |
| ISBN | : 9788170870760 |
| Author | : C. Brezinski |
| Publisher | : Elsevier |
| Total Pages | : 512 |
| Release | : 2012-12-02 |
| Genre | : Mathematics |
| ISBN | : 0444598588 |
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
| Author | : Martha Abell |
| Publisher | : Springer Nature |
| Total Pages | : 373 |
| Release | : 2019-10-21 |
| Genre | : Mathematics |
| ISBN | : 3030122778 |
Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.
| Author | : David Ronald Kincaid |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 810 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821847880 |
This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
| Author | : Sabir Umarov |
| Publisher | : Springer |
| Total Pages | : 446 |
| Release | : 2015-08-18 |
| Genre | : Mathematics |
| ISBN | : 3319207717 |
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
| Author | : Ognyan Kounchev |
| Publisher | : Academic Press |
| Total Pages | : 513 |
| Release | : 2001-06-11 |
| Genre | : Mathematics |
| ISBN | : 0080525008 |
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property
| Author | : Klaus Ritter |
| Publisher | : Springer |
| Total Pages | : 255 |
| Release | : 2007-05-06 |
| Genre | : Mathematics |
| ISBN | : 3540455922 |
The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.
| Author | : Victor A. Sadovnichiy |
| Publisher | : Springer Nature |
| Total Pages | : 525 |
| Release | : 2020-11-24 |
| Genre | : Mathematics |
| ISBN | : 303050302X |
This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields
