Operator Theory: Advances and Applications, 111. Birkhäuser, Basel, 2000.  G. Heinig, K. Rost, Hartley transform representations of symmetric Toeplitz matrix inverses with application to fast matrix-vector multiplication.
Author: Dario Andrea Bini
Publisher: Springer Science & Business Media
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
Since the coefficient matrix has integer elements we use a reflexive g-inverse with special integral properties in determining a solution. See Krishnamurthy . Since this method is not based on the chemical concept of ...
Author: R. T. Gregory
Publisher: Springer Science & Business Media
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel . Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
AN IMPLICITLY RESTARTED BIDIAGONAL LAN CZOS METHOD FOR, LARGE-SCALE SINGULAR VALUE PROBLEMS XIAOHUI WANG AND HONGYUAN ... 1 Introduction Low rank approximation of a large, sparse matrix A € 7&” is very important in many applications as ...
Author: Oleg P Iliev
Publisher: World Scientific
This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications. Contents: Computational Issues in Large Scale Eigenvalue ProblemsCombustion Modeling in Industrial FurnacesMonte Carlo MethodsMultilevel Methods for Incompressible Viscous FlowsApproximation of Nonlinear and Functional PDEsSolving Linear Systems with Error ControlRegular Numerical Methods for Inverse and Ill-Posed ProblemsMultifield ProblemsParallel and Distributed Numerical Computing with ApplicationsParameter-Robust Numerical Methods for Singularly Perturbed and Convection-Dominated ProblemsFinite Difference MethodsFinite Element MethodsFinite Volume MethodsBoundary Element MethodsNumerical Linear AlgebraNumerical Methods for Nonlinear ProblemsNumerical Methods for Multiscale ProblemsMultigrid and Domain DecompositionComputational Fluid DynamicsMathematical Modelling in Structural MechanicsEnvironmental ModellingEngineering Applications Readership: Researchers in applied mathematics and computational physics. Keywords:Numerical Methods and Applications;General Finite Difference;General Numerical Linear Algebra;Parallel Computations;Nonlinear Problems and Multiscale Methods
Freeman, San Francisco (1963) Faddeeva, V.N.: Computational Methods of Linear Algebra. Dover Books on Advanced Mathematics. Dover Publications, New York (1959) Fan, K.: Inequalities for the sum of two M-matrices. In: Shisha, O. (ed.) ...
Author: P.N. Shivakumar
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.
McCormick, C. W., "Application of partially banded matrix methods to structural analysis," pp. 155-158 in Sparse Matrix Proceedings [Willoughby (1968A) ]. Marchuk, G. I., "Some applications of splitting-up methods to the solution of ...
Author: D. Rose
Publisher: Springer Science & Business Media
This book contains papers on sparse matrices and their appli cations which were presented at a Symposium held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York on September 9-10, 1971. This is a very active field of research since efficient techniques for handling sparse matrix calculations are an important aspect of problem solving. In large scale problems, the feasibility of the calculation depends critically on the efficiency of the underlying sparse matrix algorithms. An important feature of the conference and its proceedings is the cross-fertilization achieved among a broad spectrum of application areas, and among combinatorialists, numerical analysts, and computer scientists. The mathematical, programming, and data management features of these techniques provide a unifying theme which can benefit readers in many fields. The introduction summarizes the major ideas in each paper. These ideas are interspersed with a brief survey of sparse matrix technology. An extensive unified bibliography is provided for the reader interested in more systematic information. The editors wish to thank Robert K. Brayton for his many helpful suggestions as chairman of the organizing committee and Redmond O'Brien for his editorial and audio-visual assistance. We would also like to thank Mrs. Tiyo Asai and Mrs. Joyce Otis for their help during the conference and on the numerous typing jobs for the manuscript. A special thanks goes to William J. Turner for establishing the IBM Research Symposia Series with Plenum Press.
“Linear Programming: Methods and Applications.” McGraw-Hill, New York. Gear, C. W. (1971). Simultaneous numerical solution of differential-algebraic equations, IEEE Trans. Circuit Theory CT 18, 89–95. George, J. A. (1971).
Moreover, the effect of Splitting on the rate of convergence of the methods presented is studied for matrices of class K . In ... The discussion includes the power method and its application to the inverse iteration, the Krylov method, ...
Author: Miroslav Fiedler
Publisher: Courier Corporation
This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition.
(1993), 'A note on nested dissection for rectangular grids', SIAM Journal on Matrix Analysis and Applications 14, 253–258. Björck, ̊A. (1987), 'Stability analysis of the method of seminormal equations for least squares problems', ...
Author: I. S. Duff
Publisher: Oxford University Press
The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
R. M. Thrall and L. Tornheim, “ Vector Spaces and Matrices.” Wiley, New York, 1957. 35. M. C. Pease, III, “Methods of Matrix Algebra.” Academic Press, New York, 1965. 36. R. K. Eisenschitz, “ Matrix Algebra for Physicists.
Author: J Killingbeck
Mathematical Techniques and Physical Applications provides a wide range of basic mathematical concepts and methods, which are relevant to physical theory. This book is divided into 10 chapters that cover the different branches of traditional mathematics. This book deals first with the concept of vector, matrix, and tensor analysis. These topics are followed by discussions on several theories of series relevant to physics; the fundamentals of complex variables and analytic functions; variational calculus for presenting the basic laws of many branches of physics; and the applications of group representations. The final chapters explore some partial and integral equations and derivatives of physics, as well as the concept and application of probability theory. Physics teachers and students will greatly appreciate this book.
References  Arnoldi, W. The principle of minimized iterations in the solution of the matrix eigenvalue problem. ... in Computational Techniques and Applications: CTAC '93 (Canberra, Australia, 1994), D. Stewart, H. Gardner, ...