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Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper differs from Stewart's classical result and sometimes yields tighter bounds. Moreover, we provide norm estimates for t ...
This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...
This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...
We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness fo ...
We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...
In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil , that is, A, B are Hermitian and there is a shift such that is definite. Our new meth ...
Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...
Fusion proteins containing a first domain and a second domain, where the first domain contains a crosslinkable substrate domain and the second domain contains a fibrinolysis inhibitor, are provided. In a preferred embodiment, the fibrinolysis inhibitor is ...
Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this wor ...
A generalized matrix product can be formally written as Lambda(sp)(p) Lambda(sp-1)(p-1) ... Lambda(s2)(2) Lambda(s1)(1) where s(i) is an element of {- 1,+ 1} and ( A(1), ..., A(p)) is a tuple of ( possibly rectangular) matrices of suitable dimensions. The ...