A Jacobi--Davidson Method for Solving Complex Symmetric Eigenvalue Problems

Arbenz, Peter; Hochstenbach, Michiel E.

doi:10.1137/s1064827502410992

Cited by 33 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1], Arbenz and Hochstenbach suggest a variant of the Jacobi-Davidson algorithm for complex symmetric eigenvalue problems. In this method, the standard Rayleigh quotient estimate of the eigenvalue,…”

Section: Perfectly-matched Layers and Symmetry-preserving Projectionmentioning

confidence: 99%

Model Reduction for RF MEMS Simulation

Bindel

Bai

Demmel

2006

Applied Parallel Computing. State of the Art in Scientific Computing

View full text Add to dashboard Cite

Abstract. Radio-frequency (RF) MEMS resonators, integrated into CMOS chips, are of great interest to engineers planning the next generation of communication systems. Fast simulations are necessary in order to gain insights into the behavior of these devices. In this paper, we discuss two structure-preserving model-reduction techniques and apply them to the frequency-domain analysis of two proposed MEMS resonator designs.

show abstract

Section: Perfectly-matched Layers and Symmetry-preserving Projectionmentioning

confidence: 99%

Model Reduction for RF MEMS Simulation

Bindel

Bai

Demmel

2006

Applied Parallel Computing. State of the Art in Scientific Computing

View full text Add to dashboard Cite

show abstract

“…Hence we have that the difference between the two Green's functions isG which can be written as (16). ✷ Corollary : LetG 1 (β, z, z ) satisfy the ORBC (10) andG 2 (β, z, z ) satisfy the ArBC (13).…”

Section: The Grounded Hankel Domainmentioning

confidence: 99%

“…Since P is complex symmetric, in other words P = P T (but not Hermitian symmetric: P = P * in general), the eigenvectors can be chosen to be complex orthonormal [16], i.e., Q T Q = I, in conformity with the b−orthonormality requirement DD T = I, see (69). Next we discuss the important Dirichlet and Neumann cases.…”

Section: Eigenexpansionsmentioning

confidence: 99%

Optimizing Green's Functions in Grounded Layered Media With Artificial Boundary Conditions

Knockaert¹

2006

PIER

View full text Add to dashboard Cite

Abstract-Artificial boundary conditions, which can be identified as Robin boundary conditions positioned at a complex space coordinate, are introduced in order to obtain pertinent approximations for the Green's functions in grounded layered media. These artificial boundary conditions include perfectly matched layers backed by perfectly electric or magnetic conductors. As a first result, we obtain analytical expressions for the differences of Green's functions subject to different boundary conditions. Since weighted sums of Green's functions are again Green's functions, the need arises to solve an optimization problem, in the sense of obtaining the optimal weighted mixture of Green's functions, as compared to the exact Green's function. Comprehensive eigenexpansions for the Green's functions are given in the general case, and a few examples illustrate the goodness of fit between the approximate Green's functions and the exact Green's function.

show abstract

“…Various projection methods for solving complex symmetric EVPs have been proposed, for example, based on modifications of the nonHermitian Lanczos method [3,8,9], on subspace iteration [10], or on variants of the Jacobi-Davidson method [11].…”

Section: Introductionmentioning

confidence: 99%

Non-splitting Tridiagonalization of Complex Symmetric Matrices

Gansterer

Gruber

Pacher

2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract.A non-splitting method for tridiagonalizing complex symmetric (non-Hermitian) matrices is developed and analyzed. The main objective is to exploit the purely structural symmetry in terms of runtime performance. Based on the analytical derivation of the method, Fortran implementations of a blocked variant are developed and extensively evaluated experimentally. In particular, it is illustrated that a straightforward implementation based on the analytical derivation exhibits deficiencies in terms of numerical properties. Nevertheless, it is also shown that the blocked non-splitting method shows very promising results in terms of runtime performance. On average, a speed-up of more than three is achieved over competing methods. Although more work is needed to improve the numerical properties of the non-splitting tridiagonalization method, the runtime performance achieved with this non-unitary tridiagonalization process is very encouraging and indicates important research directions for this class of eigenproblems.

show abstract

A Jacobi--Davidson Method for Solving Complex Symmetric Eigenvalue Problems

Cited by 33 publications

References 31 publications

Model Reduction for RF MEMS Simulation

Model Reduction for RF MEMS Simulation

Optimizing Green's Functions in Grounded Layered Media With Artificial Boundary Conditions

Non-splitting Tridiagonalization of Complex Symmetric Matrices

Contact Info

Product

Resources

About