نتایج جستجو برای: quadratic eigenvalue
تعداد نتایج: 64749 فیلتر نتایج به سال:
This paper is concerned with bounds for the linear response eigenvalue problem for H = [ 0 K M 0 ] , where K and M admits a 2 × 2 block partitioning. Bounds on how the changes of its eigenvalues are obtained when K and M are perturbed. They are of linear order with respect to the diagonal block perturbations and of quadratic order with respect to the off-diagonal block perturbations in K and M ...
We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is e...
We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. T...
We derive formulas for the backward error of an approximate eigenvalue of a ∗palindromic matrix polynomial with respect to ∗-palindromic perturbations. Such formulas are also obtained for complex T -palindromic pencils and quadratic polynomials. When the T -palindromic polynomial is real, then we derive the backward error of a real number considered as an approximate eigenvalue of the matrix po...
Primal-dual pairs of semideenite programs provide a general framework for the theory and algorithms for the trust region subproblem (TRS). This latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and, therefore, it is a generalization of the minimum eigenvalue problem. The importance of (TRS) is due to the fact that it provides the step in...
This two-part paper treats the numerical approximation of a tricky quadratic eigenvalue problem arising from the following generalization of the classical Taylor-Couette problem: A viscous incompressible fluid occupies the region between a rigid inner cylinder and a deformable outer cylinder, which we take to be a nonlinearly viscoelastic membrane. The inner cylinder rotates at a prescribed ang...
The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real valued critical delays, i.e...
In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. We introduce a block Jacobi-like method. This method uses only real arithmetic and orthogonal similarity transformations and achieves ultimate quadratic convergence. A theoretical analysis is conducted and some experimental results are presented.
3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...
For a given subspace, the q-Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the q-Rayleigh-Ritz method defines the q-Ritz values and the q-Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the...
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