共查询到20条相似文献,搜索用时 15 毫秒
1.
For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for solving such problems. In this study, from the analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we conclude that the Rayleigh–Ritz-type of the contour integral spectral projection method is mathematically equivalent to the Arnoldi method with the projected vectors obtained from the contour integration. By this Arnoldi-based interpretation, we then propose a block Arnoldi-type contour integral spectral projection method for solving the eigenvalue problem. 相似文献
2.
M.M.R. Williams 《Applied mathematics and computation》2010,215(11):3906-3928
We present a novel approach for calculating stochastic eigenvalues of differential and integral equations as well as for random matrices. Five examples based on very different types of problem have been analysed and detailed numerical results obtained. It would seem that the method has considerable promise. The essence of the method is to replace the stochastic eigenvalue problem λ(ξ)?(ξ)=A(ξ)?(ξ), where ξ is a set of random variables, by the introduction of an auxiliary equation in which . This changes the problem from an eigenvalue one to an initial value problem in the new pseudo-time variable t. The new linear time-dependent equation may then be solved by a polynomial chaos expansion (PCE) and the stochastic eigenvalue and its moments recovered by a limiting process. This technique has the advantage of avoiding the non-linear terms in the conventional method of stochastic eigenvalue calculation by PCE, but it does introduce an additional, ‘pseudo-time’, independent variable t. The paper illustrates the viability of this approach by application to several examples based on realistic problems. 相似文献
3.
The well-known logarithmic-quadratic proximal (LQP)method has motivated a number of efficient numerical algorithms for solving
nonlinear complementarity problems (NCPs). In this paper,we aim at improving one of them, i.e., the LQP-based interior prediction-correction
method proposed in [He, Liao and Yuan, J. Comp. Math., 2006, 24(1): 33–44], via identifying more appropriate step-sizes in
the correction steps. Preliminary numerical results for solving some NCPs arising in traffic equilibrium problems are reported
to verify the theoretical assertions. 相似文献
4.
B. M. Podlevskii 《Computational Mathematics and Mathematical Physics》2007,47(11):1745-1755
Iterative algorithms for finding two-sided approximations to the eigenvalues of nonlinear algebraic eigenvalue problems are examined. These algorithms use an efficient numerical procedure for calculating the first and second derivatives of the determinant of the problem. Computational aspects of this procedure as applied to finding all the eigenvalues from a given complex-plane domain in a nonlinear eigenvalue problem are analyzed. The efficiency of the algorithms is demonstrated using some model problems. 相似文献
5.
In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNMmin and SNMFB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201–213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125–137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method. 相似文献
6.
JeanPaul Chehab Roger Temam 《Numerical Methods for Partial Differential Equations》1995,11(3):199-228
In this article, we present several numerical multilevel schemes for the solution of nonlinear eigenvalue problems. Using the Incremental Unknowns, we construct some generalization of the Marder and Weitzner method, which is well suited for the calculation of unstable solutions. The new methods that we present are based on a different treatment of the several structures appearing with the utilization of the hierarchical preconditioner. We illustrate the efficiency of the new methods with the calculation of unstable solutions of a reaction diffusion problem. © 1995 John Wiley & Sons, Inc. 相似文献
7.
We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method. 相似文献
8.
Daniel Kressner 《Numerische Mathematik》2009,114(2):355-372
We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences
from the linear case is that distinct eigenvalues may have linearly dependent eigenvectors or even share the same eigenvector.
This has been a severe hindrance in the development of general numerical schemes for computing several eigenvalues of a nonlinear
eigenvalue problem, either simultaneously or subsequently. The purpose of this work is to show that the concept of invariant
pairs offers a way of representing eigenvalues and eigenvectors that is insensitive to this phenomenon. To demonstrate the
use of this concept in the development of numerical methods, we have developed a novel block Newton method for computing such
invariant pairs. Algorithmic aspects of this method are considered and a few academic examples demonstrate its viability. 相似文献
9.
Bartur Jumarhon Wilson Lamb Sean McKee Tao Tang 《Numerical Methods for Partial Differential Equations》1996,12(2):265-281
It is observed that the one-dimensional heat equation with certain nonlinear boundary conditions can be reformulated as a system of coupled Volterra integral equations. A product trapezoidal scheme is proposed for the numerical solution of this integral equation system, and some numerical experiments are given to compare the performances of this integral equation approach and the Crank-Nicholson method applied to the original initial-boundary value problem. © 1996 John Wiley & Sons, Inc. 相似文献
10.
In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution. 相似文献
11.
Roman I. Andrushkiw 《Applicable analysis》2013,92(1-4):211-220
Let H Be a complex and separable Hilbert space and consider in H the nonlinear eigenvalue problem where A, B, and C belong to the class of unbounded nonsymmetric operators, which are K- positive K-symmetric. Sufficient conditions insuring the existence of the eigenvalues of (i) are investigated. An iterative method for approximating the eigenvalues of (i) is developed and its convergence proved. Some numerical examples are given to illustrate the theory. 相似文献
12.
Tetsutaro Shibata 《Results in Mathematics》2004,46(1-2):130-145
We consider the nonlinear eigenvalue problem motivated by the perturbed elliptic sine-Gordon equation where p >1 is a constant and λ ∈ R is an eigenvalue parameter. Our aim is to clarify the asymptotic relationship between L p+1-norm, L ∞-norm of the solutions and λ when these norms are large. To this end, we consider an associated variational problem with this equation on a manifold new parameter), and obtain a solution pair . We establish the precise asymptotic formulas for . 相似文献
13.
A. A. Abramov 《Computational Mathematics and Mathematical Physics》2011,51(1):35-39
A modification of the method proposed earlier by the author for solving nonlinear self-adjoint eigenvalue problems for linear
Hamiltonian systems of ordinary differential equations is examined. The basic assumption is that the initial data (that is,
the system matrix and the matrices specifying the boundary conditions) are monotone functions of the spectral parameter. 相似文献
14.
15.
The Josephy-Newton method attacks nonlinear complementarity problems which consists of solving, possibly inexactly, a sequence of linear complementarity problems. Under appropriate regularity assumptions, this method is known to be locally (superlinearly) convergent. Utilizing the filter method, we presented a new globalization strategy for this Newton method applied to nonlinear complementarity problem without any merit function. The strategy is based on the projection-proximal point and filter methodology. Our linesearch procedure uses the regularized Newton direction to force global convergence by means of a projection step which reduces the distance to the solution of the problem. The resulting algorithm is globally convergent to a solution. Under natural assumptions, locally superlinear rate of convergence was established. 相似文献
16.
Alexander G. Ramm Alexandra B. Smirnova 《Numerical Functional Analysis & Optimization》2013,34(3-4):317-332
A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization parameter is introduced. A convergence theorem is proved. The proposed method is illustrated by a numerical example in which a nonlinear inverse problem of gravimetry is considered. Based on the results of the numerical experiments practical recommendations for the choice of the regularization parameter are given. Some other iterative schemes are considered. 相似文献
17.
N. Gnaneshwar 《Advances in Computational Mathematics》2007,27(3):339-354
We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by a degenerate kernel
method. By interpolating the kernel of the integral operator in both the variables, we prove that the error bounds for eigenvalues
and for the distance between the spectral subspaces are of the orders h
2r
and h
r
respectively. By iterating the eigenfunctions we show that the error bounds for eigenfunctions are of the orders h
2r
. We give the numerical results.
相似文献
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