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Author: Federico Poloni Publisher: Springer Science & Business Media ISBN: 8876423842 Category : Mathematics Languages : en Pages : 241
Book Description
This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.
Author: Federico Poloni Publisher: Springer Science & Business Media ISBN: 8876423842 Category : Mathematics Languages : en Pages : 241
Book Description
This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.
Author: Amit Bhaya Publisher: SIAM ISBN: 9780898718669 Category : Mathematics Languages : en Pages : 297
Book Description
Control Perspectives on Numerical Algorithms and Matrix Problems organizes the analysis and design of iterative numerical methods from a control perspective. The authors discuss a variety of applications, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems, support vector machines, integration and shooting methods for ordinary differential equations, matrix preconditioning, matrix stability, and polynomial zero finding. This book opens up a new field of interdisciplinary research that should lead to insights in the areas of both control and numerical analysis and shows that a wide range of applications can be approached from, and benefit from, a control perspective.
Author: Roger Even Bove Publisher: ISBN: Category : Algorithms Languages : en Pages : 118
Book Description
The following paper represents work to date on the deformation method for quadratic programming and thus may be regarded as a sequel to Zahl, S. (1964) A Deformation Method for Quadratic Programming, Research Note AFCRL-63-132. It gives an explanation of a modified Iverson programming language and uses this to give a detailed algorithm for the Zahl Deformation Method of Quadratic Programming.
Author: Oskari Heikki Ajanki Publisher: ISBN: 9781470454142 Category : Electronic books Languages : en Pages : 133
Book Description
The authors consider the nonlinear equation -\frac 1m=z+Sm with a parameter z in the complex upper half plane \mathbb H , where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in \mathbb H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on \mathbb R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur.
Author: Philippe G. Ciarlet Publisher: Cambridge University Press ISBN: 9780521339841 Category : Computers Languages : en Pages : 456
Book Description
The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.
Author: Dario A. Bini Publisher: SIAM ISBN: 9781611972092 Category : Mathematics Languages : en Pages : 266
Book Description
This treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted. Readers will find a unified discussion of doubling algorithms, which are effective in solving algebraic Riccati equations as well as a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB codes. This will help the reader gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.
Author: Aaart R. Heesterman Publisher: Springer ISBN: Category : Business & Economics Languages : en Pages : 816
Book Description
This book provides an introduction to the theory and application of a range of mathematical programming algorithms, a nd to the prerequisite fields of linear algebra and the graphical presentation of a number of rational functions. The algorithms offered cover matrix inversion, linear programming, quadratic programming with linear side-conditions, quadratic programming with quadratic side-conditions, and integer programming. The resolution of mixed systems of equations and inequalities; systems with sign-constrained and free variables; and the accommodation of upper and lower limbs in specified variables without explicitly written restrictions are discussed, for linear programming, as well as for quadratic programming with linear side-conditions. Of the algorithms provided, the sequentially constrained maximization method for solving the general quantitive programming problem is, in part, novel. The other algorithms are, in outline, established methods. There is however, a more direct approach to the problem of the infeasible starting solution and, as a result, a less rigid separation between the traditional I and II than is usual.
Author: Stephen Boyd Publisher: Cambridge University Press ISBN: 1316518965 Category : Business & Economics Languages : en Pages : 477
Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Zdenek Dostál Publisher: Springer Science & Business Media ISBN: 0387848061 Category : Mathematics Languages : en Pages : 293
Book Description
Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Author: Federico Poloni
Author: Federico Poloni
Author: Amit Bhaya
Author: Roger Even Bove
Author: Oskari Heikki Ajanki
Author: Philippe G. Ciarlet
Author: T. Kailath
Author: Dario A. Bini
Author: Aaart R. Heesterman
Author: Stephen Boyd
Author: Zdenek Dostál