The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical in linear time-invariant systems with static state feedback. In this article, we study the MGEAP when feedback has arbitrary sparsity constraints. We formulate sparse as an equality-constrained optimization and present analytical characterization of its locally optimal solution terms eigenvector matrices closed...

We propose a first-order method to solve the cubic regularization subproblem (CRS) based on novel reformulation. The reformulation is constrained convex optimization problem whose feasible region admits an easily computable projection. Our requires computing minimum eigenvalue of Hessian. To avoid expensive computation exact eigenvalue, we develop surrogate where replaced with approximate one. ...

We present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product ...

The Lanczos method is often used to solve a large and sparse symmetric matrix eigenvalue problem. It is well-known that the single-vector Lanczos method can only find one copy of any multiple eigenvalue. To compute all or some of the copies of a multiple eigenvalue, one has to use the block Lanczos method which is also known to compute clustered eigenvalues much faster than the single-vector La...