Product Description

This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework.

The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition.

This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.

Product Description

This book covers all the steps from identification of operations and resources to the transformation of virtual models into real-world algorithms. The matrix-based approach presented here is a solution to the real-time application of control in discrete event systems and flexible manufacturing systems (FMS), and offers a sound practical basis for the design of controllers for manufacturing systems.

Product Description
This work presents some classical as well as some very recentresults and techniques concerning the spectral geometry correspondingto the Laplace--Beltrami operator and the Hodge--de Rhamoperators. It treats many topics that are not usually dealt with in this field,such as the continuous dependence of the eigenvalues with respect tothe Riemannian metric in the C-topology, and some of theirconsequences, such as Uhlenbeck's genericity theorem; examples ofnon-isometric flat tori in all dimensions greater than or equal tofour; Gordon's classical technique for constructing isospectral closedRiemannian manifolds; a detailed presentation of Sunada's techniqueand Pesce's approach to isospectrality; Gordon and Webb's example ofnon-isometric convex domains in Rn (n>=4) thatare isospectral for both Dirichlet and Neumann boundary conditions;the Chanillo--Treves estimate for the first positiveeigenvalue of the Hodge--de Rham operator, etc. Significantapplications are developed, and many open problems, references andsuggestions for further reading are given. Several themes foradditional research are pointed out. Audience: This volume is designed as an introductory text formathematicians and physicists interested in global analysis, analysison manifolds, differential geometry, linear and multilinear algebra,and matrix theory. It is accessible to readers whose backgroundincludes basic Riemannian geometry and functional analysis. Thesemathematical prerequisites are covered in the first two chapters, thusmaking the book largely self-contained. ... Read more

Product Description
Die "Wirtschaftsmathematik" ist eine Zusammenfassung der in den Wirtschaftswissenschaften gemeinhin benötigten mathematischen Kenntnisse. Band 2, Analysis I, dient der Wiederholung/Vertiefung des gymnasialen Oberstufenstoffes. Hier wird der Funktionsbegriff, werden Folgen und Reihen, die Differentialrechnung und die Integralrechnung von Funktionen einer Variablen eingeführt. Ziel der behandelten Mathematik ist die Erarbeitung wichtiger Werkzeuge zur ökonomischen Analyse: ökonomische Funktionen, Renten- und Zinseszinsrechnung, Untersuchungen über Kosten- oder Ertragsänderungen, Aggregation von Geldströmen etc. Die fernstudienerfahrenen Autoren haben den Stoff so aufbereitet, daß das Buch für das Selbststudium besonders geeignet ist. ... Read more

Product Description
Das Standardwerk für Ingenieure, Naturwissenschaftler und Informatiker jetzt in der 6. Auflage: Band 1 des zweibändigen Lehrbuchs Höhere Mathematik. Neben dem üblichen Vorlesungsstoff bieten die Autoren auch weiterführende Anregungen. Dieser Band umfasst neben Differential- und Integralrechnung für Funktionen in einer und mehreren reellen Variablen auch Vektoranalysis, Integralsätze und die n-dimensionale Vektor- und Matrizenrechnung. Eine Fülle eindrucksvoller Abbildungen, praxisbezogener Beispiele und Übungsaufgaben tragen zur Anschaulichkeit bei. Besonders gekennzeichnete Zusammenfassungen mit detaillierten Rechenschemata eignen sich hervorragend zur Prüfungsvorbereitung.
"Ein glänzendes Buch, das durch seine präzise und doch anschauliche Darstellung, vor allem aber durch die Vielfalt der enthaltenen Beispiele, aus der großen Zahl von Werken ähnlicher Zielrichtung hervortritt. " Int. Math. Nachr. Österreich ... Read more

Customer Reviews (1)

Good reference for deciding which method fits your problem
The book gives good insights about choosing particular methods. The author shows many tables comparing different strategies and matrices. The reader doesn't need to have background on sparse matrices.It is really a`cookbook' on sparse matrix solutions. ... Read more

Product Description
The symplectic eigenvalue problem is helpful, e.g., inanalyzing a number of different questions that arise in linear controltheory for discrete-time systems. Industrial production andtechnological processes may suffer from unwanted behavior, e.g.,losses in the start-up and change-over phases of operation, pollution,emission of harmful elements, and production of unwanted by-products.Control techniques offer the possibility of analyzing such processesin order to detect the underlying causes of the unwanted behavior.This monograph describes up-to-date techniques for solving small tomedium-sized as well as large and sparse symplectic eigenvalueproblems. The text presents all developed algorithms inMatlab-programming style and numerical examples to demonstrate theirabilities, all of which makes the text accessible to graduate studentsin applied mathematics and control engineering, as well as toresearchers in these areas. ... Read more

Product Description
In response to a growing interest in Total Least Squares (TLS)and Errors-In-Variables (EIV) modeling by researchers andpractitioners, well-known experts from several disciplines wereinvited to prepare an overview paper and present it at the thirdinternational workshop on TLS and EIV modeling held in Leuven,Belgium, August 27-29, 2001. These invited papers, representingtwo-thirds of the book, together with a selection of other presentedcontributions yield a complete overview of the main scientificachievements since 1996 in TLS and Errors-In-Variables modeling. Inthis way, the book nicely completes two earlier books on TLS (SIAM1991 and 1997). Not only computational issues, but also statistical,numerical, algebraic properties are described, as well as many newgeneralizations and applications. Being aware of the growing interestin these techniques, it is a strong belief that this book will aid andstimulate users to apply the new techniques and models correctly totheir own practical problems. ... Read more

Product Description

Cost estimating is a powerful tool in industry and business. Anyone involved in cost estimating will find this book extremely useful because of the real life examples, which mean they can use the information in real situations immediately.

Product Description
This is the first book on higher dimensional Hadamard matrices and their applications in telecommunications and information security. It is divided into three parts according to the dimensions of the Hadamard matrices treated. ... Read more

Product Description

This volume aims to provide the fundamental knowledge to appreciate the advantages of the J-matrix method and to encourage its use and further development. The J-matrix method is an algebraic method of quantum scattering with substantial success in atomic and nuclear physics. The accuracy and convergence property of the method compares favourably with other successful scattering calculation methods. Despite its thirty-year long history new applications are being found for the J-matrix method.

This book gives a brief account of the recent developments and some selected applications of the method in atomic and nuclear physics. New findings are reported in which experimental results are compared to theoretical calculations. Modifications, improvements and extensions of the method are discussed using the language of the J-matrix.

The volume starts with a Foreword by the two co-founders of the method, E.J. Heller and H.A. Yamani and it contains contributions from 24 prominent international researchers.

Product Description

Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

Product Description

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in Computational Mathematics who have written various successful books.

Product Description

This book reviews new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. It provides the reader with rigorous and in-depth mathematical analysis of the uses of polynomial and rational matrices in the study of dynamical systems. It also throws new light on the problems of positive realization, minimum-energy control, reachability, and asymptotic and robust stability.

Product Description

This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.

Product Description

This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics.

This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

Product Description
This book is unique.It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries to the most recent 20th century developments.Several contributions have never been published before. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors.They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis.The whole of Chapter 4 is devoted to particular determinants including alternants, Wronskians and Hankelians.The contents of Chapter 5 include the Cusick and Matsuno identities. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory.They include the KdV, Toda and Einstein equations.The solutions are verified by applying theorems established in earlier chapters and in the extensive appendix. The book ends with an extensive bibliography and an index. Mathematicians, physicists and engineers who wish to become acquainted with modern developments in the analytic theory of determinants will find the book indispensable. ... Read more

Customer Reviews (1)

Vein and Dale's Determinants and Applications
This book, as usual by the excellent Springer publishers, continues the trend launched by the Clifford algebra people (Lounesto, Chisholm, Baylis, Pezzaglia, Okubo, Benn, etc. - see reviews of some of them), namely, toSIMPLIFY the mathematics of physics by using appropriate ALGEBRAICtechniques rather than geometry or calculus or other techniques.Both thisbook by Vein and Dale and the Clifford algebra books and papers use algebrain physics largely to replace hard to manipulate geometry and unwieldlymatrices.A matrix is an algebraic quantity, but it is very hard tohandle: it is essentially a table of numbers, for example a table ofpeople's heights, or people's heights by weights.You add tables by addingcorresponding positions in each table, and likewise for subtracting, whilemultiplication is much more complicated.However, as Vein and Dale show,you can replace many results in physics which involve matrices byDETERMINANTS. A determinant is a single number, typically, which is gottenby combining the numbers of the matrix table in a certain way given by aformula.Thus, replacing a matrix by a determinant means replacing a tableby a single number.It turns out that the Einstein Equation(s) of generalrelativity can be solved in this way (for the axially symmetric field), andlikewise for equations involving solitary waves (Kadomtsev-Petashviliequation), waves in a rotating fluid (Benjamin-Ono equation), etc.Animportant tool in this process is Backlund transformations, which aredescribed in the appendix but are more thoroughly described in the 1989book of Bluman and Kumei which (together with their journal publications)initiated much of the simplification of differential equations of themodern era.That book, as you may guess, was also published bySpringer/Springer-Verlag. ... Read more

Product Description
This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and offering over 350 exercises, it is well-suited as a textbook for beginners at graduate level. With its extensive bibliography covering about 500 research papers, this text is also an ideal reference book for the professional researcher. The subdivision of the contents into 21 more or less independent chapters enables readers to familiarize themselves quickly with a specific topic, and facilitates the use of this book as a basis for complementary courses in other areas such as computer algebra. ... Read more

Customer Reviews (1)

An Excellent Introduction and Reference
This book presents an excellent and thorough introduction and overview of the field.It contains results of 573 papers in the field, but requires few prerequisites beyond basic abstract and linear algebra. It's perfect for independent study.

The key parts of the book for those interested in the matrix multiplication problem, like myself, and related problems are chapters 14-18. Chapter 14 describes the theory of the multiplicative complexity of bilinear maps, of which matrix multiplication is one, in terms of the concept of rank (also tensor rank), especially in the context of matrix algebras. The rank of a bilinear map is essentially a measure of the minimum number of multiplications in a bilinear algorithm for computing the map. Chapter 15 introduces the exponent of matrix multiplication in relation to the asymptotic complexity of the latter, and describes the fundamental relations between these asymptotic and bilinear measures, including the proof of Schonhage's important asymptotic direct sum inequality. Chapter 16 shows the fundamental importance of the exponent because it is found to determine the complexities of other important matrix operations such as inversion, taking of determinants, computing of characteristic polynomials etc. Chapters 17 and 18 describe further extensions, applications and links, including an interesting link between the ranks of finite fields and the minimal distances of linear error-correcting codes. ... Read more

Product Description

This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.

Customer Reviews (1)

An excellent book
This book is well-written and the authors explain the relationship amonggeneralized inverses very clearly, unlike some other books. ... Read more