Download or read book Advanced Methods for Solving Nonlinear Eigenvalue Problems of Generalized Phase Optimization written by Mykhaylo I. Andriychuk and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the process of solving the problems of generalized phase optimization the necessity to apply an eigenvalue approach often appears. The practical statement of the optimization problems consists of using the amplitude characteristics of functions that are sought. The usual way of optimization is deriving the Euler equation of the functional, which is used as criterion of optimization. As a rule, such equation is an integral one. It is worth pointing out that the integral equations of the generalized phase optimization are nonlinear ones. The characteristic property of such equations is non-uniqueness of solutions and their branching or bifurcation. The determination of branching solutions leads to the investigation of the corresponding homogeneous equations and the respective eigenvalue problem. This problem is nonlinear because of specificity of the statement of the optimization problem. The study of the above problem allows us to determine a set of points, in which the respective eigenvalues are equal to unity that determines the branching points of solutions. The data of calculations testify to the ability of the approach proposed to determine the solutions of nonlinear equations numerically with not large computations.
Download or read book Matrix Theory written by Mykhaylo Andriychuk and published by BoD – Books on Demand. This book was released on 2023 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Theory - Classics and Advances examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science. It consists of eleven chapters divided into two sections. Section 1, "Theory and Progress", discusses the classical problems of matrix theory and its contribution to different fields of pure mathematics. Section 2, "Applications", contains the research related to the application of matrix theory in applied science.
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Download or read book Solution of Nonlinear Eigenvalue Problems Arising from Constrained Rayleigh Quotient Optimization and Resonant Modes Computation of Accelerator Cavity written by Yunshen Zhou and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two parts: constrained Rayleigh quotient optimization problems and its application in image segmentation, and Pade approximation linearization algorithm to solve nonlinear eigenvalue problems arising from resonant modes computation of accelerator cavity. In the first part, we consider the following constrained Rayleigh quotient optimization problem [formula omitted], where A is an n*n real symmetric matrix and C is an n*m real matrix. Usually, m“n. The problem is also known as the constrained eigenvalue problem in the literature because it becomes an eigenvalue problem if the linear constraint C[superscript T]x = b is removed. We start by equivalently transforming CRQopt into an optimization problem, called LGopt, of minimizing the Lagrangian multiplier of CRQopt, and then an eigenvalue problem, called QEPmin, of finding the smallest eigenvalue of a quadratic eigenvalue problem. Although such equivalences has been discussed in the literature, it appears to be the first time that these equivalences are rigorously justified. Then we propose to numerically solve LGopt and QEPmin by the Krylov subspace projection method via the Lanczos process. The basic idea, as the Lanczos method for the symmetric eigenvalue problem, is to first reduce LGopt and QEPmin by projecting them onto Krylov subspaces to yield problems of the same types but of much smaller sizes, and then solve the reduced problems by some direct methods, which is either a secular equation solver (in the case of LGopt) or an eigensolver (in the case of QEPmin). The resulting algorithm is called the Lanczos algorithm. We perform convergence analysis for the proposed method and obtain error bounds. The sharpness of the error bound is demonstrated by artificial examples, although in applications the method often converges much faster than the bounds suggest. Finally, we apply the Lanczos algorithm to semi-supervised learning in the context of constrained clustering. In the second part, we propose a method to solve nonlinear eigenvalue problems with low-rank nonlinear terms. We first apply rational approximants to the nonlinear functions and transform the nonlinear eigenvalue problem to a rational eigenvalue problem. Then we transform the rational eigenvalue problem to a linear eigenvalue problem by trimmed linearization. For solving the linear eigenvalue problem, we provide a method to compute the matrix-vector multiplication for the shift-invert Arnoldi method, which is suitable for any shift. Moreover, the method of matrix-vector multiplication is designed to make the arithmetic as real as possible. We show the effectiveness of our Pade approximate linearization (PAL) method by comparing it with the fully rational Krylov method for nonlinear eigenvalue problems (NLEIGS) and compact rational Krylov (CORK) methods to solve nonlinear eigenvalue problems arising from finite element electromagnetic simulations in accelerator modeling. For these problems, we provide a method to choose the expansion point of rational approximants to reduce the residual for the eigenpairs by up to three digits. Numerical examples show that our PAL algorithm runs 48% to 87% faster than NLEIGS and CORK algorithm with comparable results.
Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Download or read book Topological Methods for Nonlinear Eigenvalue Problems written by John Francis Toland and published by . This book was released on 1973 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Solution Methods for Nonlinear Eigenvalue Problems written by Peter Cedric Effenberger and published by . This book was released on 2013 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stanford Bulletin written by and published by . This book was released on 2006 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1967 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summaries of Projects Completed written by National Science Foundation (U.S.) and published by . This book was released on with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1985 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book System Design and Control Integration for Advanced Manufacturing written by Han-Xiong Li and published by John Wiley & Sons. This book was released on 2014-10-27 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most existing robust design books address design for static systems, or achieve robust design from experimental data via the Taguchi method. Little work considers model information for robust design particularly for the dynamic system. This book covers robust design for both static and dynamic systems using the nominal model information or the hybrid model/data information, and also integrates design with control under a large operating region. This design can handle strong nonlinearity and more uncertainties from model and parameters.
Download or read book University of Michigan Official Publication written by University of Michigan and published by UM Libraries. This book was released on 1999 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each number is the catalogue of a specific school or college of the University.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2005 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multigrid Techniques written by Achi Brandt and published by SIAM. This book was released on 2011-01-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
Download or read book Advances in Nuclear Fuel Management II written by and published by . This book was released on 1997 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
