نتایج جستجو برای: quadratic eigenvalue

تعداد نتایج: 64749  

Journal: :Comp. Opt. and Appl. 2014
Luís M. Fernandes Joaquim Júdice Hanif D. Sherali Maria Antónia Forjaz

In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice et al. [1]. Procedures for computing the interval that contains all the eigenvalues of the linear EiCP are first presented. A nonlinear programming (NLP) model for the quadratic EiCP is formulated next, and a necessary and suf...

1987
S. FRIEDLAND J. NOCEDAL M. L. OVERTON

We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem. One of these methods is new. We study the case where multiple eigenvalues are given: we show how to state the problem so that it is not overdetermined, and describe how to modify the numerical methods to retain quadratic convergence on the modif...

Journal: :SIAM J. Numerical Analysis 2002
Defeng Sun Jie Sun

It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions, which implies that the eigenvalues are semismooth functions. Based on a recent result of the authors, it is further proved in this paper that the eigenvalues of a symmetric ma...

Journal: :Math. Program. 2005
Ivo Nowak

e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...

2010
CHEN GREIF MICHAEL L. OVERTON Gene H. Golub

We characterize the spectral behavior of a primal Schur-complement-based block diagonal preconditioner for saddle point systems, subject to low-rank modifications. This is motivated by a desire to reduce as much as possible the computational cost of matrix-vector products with the (1,1) block, while keeping the eigenvalues of the preconditioned matrix reasonably clustered. The formulation leads...

2006
Steven Delvaux Luca Gemignani Marc Van Barel

n this paper we present two fast numerical methods for computing the QR factorization of a Cauchy-like matrix C with data points lying on the real axis or on the unit circle in the complex plane. It is shown that the rows of the Q-factor of C give the eigenvectors of a rank structured matrix partially determined by some prescribed spectral data. This property establishes a basic connection betw...

Journal: :Multiscale Modeling & Simulation 2003
Yehuda Koren Liran Carmel David Harel

We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimi...

2008
G. Akemann

Abstract. We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a skew-symmetric kernel from which all complex eigenvalue correlations can be derived. Our results are obtained in a very simple fashion without going to an eigenvalue representation, and are co...

Journal: :Comput. Meth. in Appl. Math. 2014
Fioralba Cakoni Peter Monk Jiguang Sun

In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions...

2007
Volker Mehrmann

We discuss optimal control problems for general unstructured linear differentialalgebraic equations of arbitrary index. We discuss controllability and observability in the higher order case and show that order reduction may lead to false results. We then derive necessary conditions in the case of linear-quadratic control problems and show how these lead to eigenvalue problems for for even matri...

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