Theory Of Difference Equations Numerical Methods And Applications By V Lakshmikantham And D Trigiante
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| Author | : Lakshmikantham |
| Publisher | : Elsevier |
| Total Pages | : 255 |
| Release | : 1988-05-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0080958699 |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
| Author | : V. Lakshmikantham |
| Publisher | : CRC Press |
| Total Pages | : 294 |
| Release | : 2002-06-12 |
| Genre | : Mathematics |
| ISBN | : 0824744241 |
"Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."
| Author | : Lakshmikantham |
| Publisher | : Elsevier |
| Total Pages | : 264 |
| Release | : 1988-04-28 |
| Genre | : Mathematics |
| ISBN | : |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
| Author | : Ravi P. Agarwal |
| Publisher | : Springer |
| Total Pages | : 218 |
| Release | : 2014-06-13 |
| Genre | : Mathematics |
| ISBN | : 3319064479 |
This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
| Author | : M.M. Rao |
| Publisher | : CRC Press |
| Total Pages | : 790 |
| Release | : 2018-10-03 |
| Genre | : Mathematics |
| ISBN | : 1482258102 |
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
| Author | : J.W. Gardner |
| Publisher | : CRC Press |
| Total Pages | : 412 |
| Release | : 2003-11-19 |
| Genre | : Mathematics |
| ISBN | : 9780203913352 |
Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.
| Author | : Ravi P. Agarwal |
| Publisher | : CRC Press |
| Total Pages | : 392 |
| Release | : 2004-08-30 |
| Genre | : Mathematics |
| ISBN | : 0203025741 |
This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq
| Author | : Eldon Hansen |
| Publisher | : CRC Press |
| Total Pages | : 528 |
| Release | : 2003-12-19 |
| Genre | : Mathematics |
| ISBN | : 9780203026922 |
Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.
| Author | : Claudia Menini |
| Publisher | : CRC Press |
| Total Pages | : 784 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 1351991469 |
In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
| Author | : Fred W. Steutel |
| Publisher | : CRC Press |
| Total Pages | : 562 |
| Release | : 2003-10-03 |
| Genre | : Mathematics |
| ISBN | : 020301412X |
Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.
