QD algorithms and algebraic eigenvalue problems
نویسندگان
چکیده
منابع مشابه
Algebraic Eigenvalue Problems
Even if both A and B are real-valued, it is likely that λ and x are complexvalued. Finding the solution of eigensystems is a fairly complicated procedure. It is at least as difficult as finding the roots of polynomials. Therefore, any numerical method for solving eigenvalue problems is expected to be iterative in nature. Algorithms for solving eigenvalue problems include the power method, subsp...
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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...
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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...
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Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges ...
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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 ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1983
ISSN: 0024-3795
DOI: 10.1016/0024-3795(83)90205-7