MULTISCALE ALGORITHMS FOR EIGENVALUE PROBLEMS
نویسندگان
چکیده
منابع مشابه
Multiscale Algorithms for Eigenvalue Problems
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and self-consistent eigenvalue problems. In principle, the expensive orthogonalization and Ritz projection operations can be moved to coarse levels, thus substantially reduci...
متن کاملAlgorithms for hyperbolic quadratic eigenvalue problems
We consider the quadratic eigenvalue problem (QEP) (λ2A+λB+ C)x = 0, where A,B, and C are Hermitian with A positive definite. The QEP is called hyperbolic if (x∗Bx)2 > 4(x∗Ax)(x∗Cx) for all nonzero x ∈ Cn. We show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the QEP. A hyperbolic QEP is overdamped if B is positive definite and C is positive ...
متن کاملQR-like Algorithms for Eigenvalue Problems
In the year 2000 the dominant method for solving matrix eigen-value problems is still the QR algorithm. This paper discusses the family of GR algorithms, with emphasis on the QR algorithm. Included are historical remarks, an outline of what GR algorithms are and why they work, and descriptions of the latest, highly parallelizable, versions of the QR algorithm. Now that we know how to paralleliz...
متن کاملA New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
متن کاملCone-constrained eigenvalue problems: theory and algorithms
Equilibria in mechanics or in transportation models are not always expressed through a system of equations, but sometimes they are characterized by means of complementarity conditions involving a convex cone. This work deals with the analysis of cone-constrained eigenvalue problems. We discuss some theoretical issues like, for instance, the estimation of the maximal number of eigenvalues in a c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Theoretical and Computational Chemistry
سال: 2003
ISSN: 0219-6336,1793-6888
DOI: 10.1142/s0219633603000665