We propose a fast stochastic Riemannian gradient eigensolver for a real and symmetric matrix, and prove its local, eigengap-dependent and linear convergence. The fast convergence is brought by deploying the variance reduction technique which was originally developed for the Euclidean strongly convex problems. In this paper, this technique is generalized to Riemannian manifolds for solving the g...

We propose a simple level set method for the Dirichlet k-partition problem which aims to partition an open domain into K different subdomains as minimize sum of smallest eigenvalue Laplace operator in each subdomain. first formulate nested minimization functional function and eigenfunction defined As approximation, we simply replace by so that can then be converted single problem. apply standar...

Computation of the inner state parameters in DSO inversion requires solving a large normal matrix system. A combined conjugate gradient and Lanczos iterative technique can be used to both solve the system and approximate some of the spectrum of the normal operator. At each iteration of the conjugate gradient algorithm, a small tridiagonal matrix (of dimension equal to the number of iterations) ...

Computation of the inner state parameters in DSO inversion requires solving a large normal matrix system. A combined conjugate gradient and Lanczos iterative technique can be used to both solve the system and approximate some of the spectrum of the normal operator. At each iteration of the conjugate gradient algorithm, a small tridiagonal matrix (of dimension equal to the number of iterations) ...

The minimization principle and Cauchy-like interlacing inequalities for the generalized linear response eigenvalue problem are presented. Based on these theoretical results, the best approximations through structure-preserving subspace projection and a locally optimal block conjugate gradient-like algorithm for simultaneously computing the first few smallest eigenvalues with the positive sign a...