Results 11 to 20 of about 675,086 (262)
Generalized eigenvalue problems with specified eigenvalues [PDF]
IMA Journal of Numerical Analysis, 2013 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 for two applications.
D. Kressner +3 more
openaire +6 more sources
Nonlinear Eigenvalue Problems with Specified Eigenvalues [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem $T$, we are concerned with finding the minimal backward error such that $T$ has a set of prescribed eigenvalues with prescribed algebraic multiplicities.
Michael Karow +2 more
openaire +5 more sources
Calculus of Variations and Partial Differential Equations, 2013 We study a non-local eigenvalue problem related to the fractional Sobolev spaces for large values of p and derive the limit equation as p goes to infinity. Its viscosity solutions have many interesting properties and the eigenvalues exhibit a strange behaviour.
Lindgren, Erik, Lindqvist, Peter
openaire +2 more sources
Biometrika, 2020 Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues.
Tyler, David E., Yi, Mengxi
openaire +2 more sources
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem [PDF]
, 2007 In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at random ...
A. Borodin +64 more
core +2 more sources
Non-Hermitian oscillators with $T_{d}$ symmetry [PDF]
, 2014 We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$.
Amore, Paolo +2 more
core +2 more sources
Graphs with many valencies and few eigenvalues [PDF]
, 2015 Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily ...
Koolen, Jack H. +2 more
core +1 more source
Journal of Statistical Physics, 2015 We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most
openaire +4 more sources
Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle [PDF]
, 2015 We address the question of determining the eigenvalues $\lambda\_n$ (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with $n$ nodal domains ...
Bérard, Pierre, Helffer, Bernard
core +5 more sources
A fully parallel method for tridiagonal eigenvalue problem
International Journal of Mathematics and Mathematical Sciences, 1994 In this paper, a fully parallel method for finding all eigenvalues of a real matrix pencil (A,B) is given, where A and B are real symmetric tridiagonal and B is positive definite. The method is based on the homotopy continuation coupled with the strategy
Kuiyuan Li
doaj +1 more source