# Spectral Variation, Normal Matrices, and Finsler Geometry

## Related Articles

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This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue...

- A random matrix model for quantum mixing. Zelditch, Steve // IMRN: International Mathematics Research Notices;1996, Vol. 1996 Issue 3, p115
The article discusses a random matrix model for quantum mixing. It formulates and proves one such kind of connection. It defines a probability spaces (UP; dvP) with UP an infinite-dimensional subgroup of the group of unitary operators on H:D LÂ²(M). It also reveals the relation of the matrix...

- Improving AOR Method for a Class of Two-by-Two Linear Systems. Cuixia Li; Shiliang Wu // Applied Mathematics;Feb2011, Vol. 2 Issue 2, p236
In this paper, the preconditioned accelerated overrelaxation (AOR) method for solving a class of two-by-two linear systems is presented. A new preconditioner is proposed according to the idea of [1] by Wu and Huang. The spectral radii of the iteration matrix of the preconditioned and the...

- A note on computing matrix geometric means. Bini, Dario Andrea; Iannazzo, Bruno // Advances in Computational Mathematics;Nov2011, Vol. 35 Issue 2-4, p175
A new definition is introduced for the matrix geometric mean of a set of k positive definite nÃ— n matrices together with an iterative method for its computation. The iterative method is locally convergent with cubic convergence and requires O( n k) arithmetic operations per step whereas the...

- Stochastic nonlinear Perron—Frobenius theorem. Evstigneev, Igor V.; Pirogov, Sergey A. // Positivity;Mar2010, Vol. 14 Issue 1, p43
We establish a stochastic nonlinear analogue of the Perronâ€“Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space and a random transformation D of the non-negative cone of an n-dimensional...

- On the bounds of the largest eigen value and the Laplacian energy of certain class of graphs. V. Lokesha; Ranjini, P. S. // Scientia Magna;2010, Vol. 6 Issue 4, p15
The energy of a graph G is defined as the sum of the eigen values of the adjacency matrix of the graph G. We report the upper Bounds for the Laplacian energy of the L(S(Kn)), L(S(Wn)), L(S(Tn,k)) and L(S(Ln)), where L and S stands for line graph and subdivision graph of G. The bounds for the...

- The Airy1 Process is not the Limit of the Largest Eigenvalue in GOE Matrix Diffusion. Bornemann, Folkmar; Ferrari, Patrik; Prähofer, Michael // Journal of Statistical Physics;Nov2008, Vol. 133 Issue 3, p405
Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy1-process, arising as a limit law in stochastic surface growth, is not the limit law for the evolution of the largest eigenvalue in GOE matrix diffusion.

- Deviation from tri-bimaximal mixings through flavour twisters in inverted and normal hierarchical neutrino mass models. Singh, N. Nimai; Rajkhowa, Monisa; Borah, Abhijit // Pramana: Journal of Physics;Oct2007, Vol. 69 Issue 4, p533
We explore a novel possibility for lowering the solar mixing angle (Î¸12) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle (Î¸23 = 45Â°) and zero reactor angle (Î¸13 = 0Â°) in the inverted and normal hierarchical neutrino mass models...

- Î¨-ASYMPTOTIC STABILITY OF NONLINEAR DIFFERENCE EQUATIONS. Rao, T. S.; Kumar, G. Suresh; Murty, M. S. N. // Far East Journal of Mathematical Sciences;Dec2013, Vol. 83 Issue 1, p21
This paper deals with obtaining sufficient conditions for Î¨-asymptotic stability of trivial solution for the linear and nonlinear difference equations on â„•. And also we provide a way to construct asymptotically stable difference equation from the given equation using Î¨ -asymptotic...