In this paper, we first give a short review of the eigenvalue estimates of Laplace operator and Schrödinger operators. Then we discuss the evolution of eigenvalues along the Ricci flow, and two new bounds of the first eigenvalue using gradient estimates. 2000 Mathematics Subject Classification: 58J50, 35P15, 53C21.

A novel method for approximating structured singular values (also known as μvalues) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eigenvalue perturbation theory. Our approach consists of an inner-outer iteration. In the outer iteration, a Newton method is used to adjust the pertu...

We developed a high speed eigenvalue solver that is an essential part of a plasma stability analysis system for fusion reactors on a Cell cluster system. In order to achieve continuous operation of fusion reactors, we must evaluate the state of plasma within the characteristic confinement time of the plasma density and temperature in fusion reactors. This is because we can prevent plasma from b...

Image restoration is often solved by minimizing an energy function consisting of a datafidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edgepreserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we Supported by The National Ba...

Second-order tensors may be described in terms of shape and orientation. Shape is quantified by tensor invariants, which are fixed with respect to coordinate system changes. This chapter describes an anatomically-motivated method of detecting edges in diffusion tensor fields based on the gradients of invariants. Three particular invariants (the mean, variance, and skewness of the tensor eigenva...

background: sperm selection for icsi based on morphology and motility might not be relevant to chromatin integrity. thus sperm selection based on sperm characteristics has been suggested. objective: the aim of this study was to compare the efficiency of zeta method with routine density gradient centrifugation method (dgc) for the selection of sperm with higher dna integrity. materials and metho...

We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices A = XX∗, where X is an N × n matrix with iid standard complex normal entries. Under the scaling n = N + b √ 4cNc, c > 0 and N →∞, we show that the rescaled fluctuations of the smallest eigenvalue, largest eigenvalue and condition number of the matrices A are all given by the Tracy–Widom distribution ...

It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required, the Conjugate Gradient method will compute the optimal approximate solution from the appropriate Krylov subspace, that is, it will implicitly compute the optimal polynomial. Henc...

abstract Lanczos's major contributions to the numerical solution of linear equations are contained in two papers: \An Iteration Method for the Solution of the Eigenvalue Problem of Linear Diierential and Integral Operators" and \Solutions of Linear Equations by Minimized Iterations ," the second of which contains the method of conjugate gradients. In this note we retrace Lanczos's journey from ...