A fully parallel method for the singular eigenvalue problem

In this paper, a fully parallel method for finding all eigenvalues of a real matrix pencil(A,B)is given, whereAandBare real symmetric tridiagonal andBis positive definite. The method is based on the homotopy continuation coupled with the strategy ?Divide-Conquer? and Laguerre iterations. The numerical results obtained from implementation of this method on both single and multiprocessor computers are presented. It appears that our method is strongly competitive with other methods. The natural parallelism of our algorithm makes it an excellent candidate for a variety of advanced architectures.

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FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EIGENVALUE PROBLEM

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30132-2 ◽

1994 ◽

Vol 14 (4) ◽

pp. 426-437

Author(s):

Liede Huang ◽

Zhonghuan Xia

Keyword(s):

Eigenvalue Problem ◽

Nonlinear Equations ◽

Fredholm Determinant

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A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo ◽

10.1051/snamc/201404206 ◽

2014 ◽

Cited By ~ 1

Author(s):

Tianyu Liu ◽

Xining Du ◽

Wei Ji ◽

X. George Xu ◽

Forrest B. Brown

Keyword(s):

Monte Carlo ◽

Eigenvalue Problem ◽

Comparative Study ◽

Monte Carlo Methods

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Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2006.11.1.14762 ◽

2006 ◽

Vol 11 (1) ◽

pp. 13-32 ◽

Cited By ~ 10

Author(s):

B. Bandyrskii ◽

I. Lazurchak ◽

V. Makarov ◽

M. Sapagovas

Keyword(s):

Differential Equation ◽

Eigenvalue Problem ◽

Variable Coefficient ◽

Order Differential Equation ◽

Integral Condition ◽

Second Order ◽

Computational Results ◽

Discrete Method ◽

Complex Eigenvalues ◽

Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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NONLINEAR EIGENVALUE PROBLEM APPROACH IN THE INTEGRAL TRANSFORMS ANALYSIS OF METAL SEPARATION BY POLYMERIC DIFFUSIVE MEMBRANES

Proceeding of Proceedings of CHT-17 ICHMT International Symposium on Advances in Computational Heat Transfer May 28-June 1, 2017, Napoli, Italy ◽

10.1615/ichmt.2017.cht-7.1390 ◽

2017 ◽

Cited By ~ 1

Author(s):

Péricles C. Pontes ◽

Anderson P. Almeida ◽

Carolina Palma Naveira-Cotta ◽

Renato M. Cotta

Keyword(s):

Eigenvalue Problem ◽

Nonlinear Eigenvalue Problem ◽

Integral Transforms ◽

Metal Separation ◽

Nonlinear Eigenvalue

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NONLINEAR EIGENVALUE PROBLEM APPROACH IN THE INTEGRAL TRANSFORMS ANALYSIS OF METAL SEPARATION BY POLYMERIC DIFFUSIVE MEMBRANES

Proceeding of Proceedings of CHT-17 ICHMT International Symposium on Advances in Computational Heat Transfer May 28-June 1, 2017, Napoli, Italy ◽

10.1615/ichmt.2017.1390 ◽

2017 ◽

Cited By ~ 1

Author(s):

Péricles C. Pontes ◽

Anderson P. Almeida ◽

Carolina Palma Naveira-Cotta ◽

Renato M. Cotta

Keyword(s):

Eigenvalue Problem ◽

Nonlinear Eigenvalue Problem ◽

Integral Transforms ◽

Metal Separation ◽

Nonlinear Eigenvalue

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On eigenvalue problem of the Laplace operators for ellipsoidal areas

Uzbek Mathematical Journal ◽

10.29229/uzmj.2018-1-15 ◽

2018 ◽

Vol 2018 (1) ◽

pp. 146-154

Author(s):

D.G. Rakhimov ◽

◽

Sh.M. Suyarov ◽

Keyword(s):

Eigenvalue Problem ◽

Laplace Operators

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Power Iterations and the Dominant Eigenvalue Problem

10.21236/ada261695 ◽

1992 ◽

Author(s):

Jeffery J. Leader

Keyword(s):

Eigenvalue Problem ◽

Dominant Eigenvalue

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Design of IIR digital filters using complex allpass network based on eigenvalue problem

Electronics Letters ◽

10.1049/el:19920143 ◽

1992 ◽

Vol 28 (3) ◽

pp. 231 ◽

Cited By ~ 1

Author(s):

X. Zhang ◽

H. Iwakura

Keyword(s):

Eigenvalue Problem ◽

Digital Filters ◽

Iir Digital Filters

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Generalized principal eigenvalues of convex nonlinear elliptic operators in ℝN

Advances in Calculus of Variations ◽

10.1515/acv-2020-0035 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Anup Biswas ◽

Prasun Roychowdhury

Keyword(s):

Eigenvalue Problem ◽

Principal Eigenvalue ◽

Unbounded Domains ◽

Elliptic Operators ◽

Maximum Principles ◽

Generalized Eigenvalues ◽

Nonlinear Elliptic ◽

Generalized Eigenvalue ◽

General Convex ◽

Appl Math

AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator which is locally elliptic and positively 1-homogeneous. Generalizing [H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.

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