Abstract The capacity for solving eigenstates with a quantum computer is key ultimately simulating physical systems. Here we propose inverse iteration eigensolvers, which exploit the power of computing classical method. A ingredient constructing an Hamiltonian as linear combination coherent evolution. We first consider continuous-variable mode (qumode) realizing such integral, weights being enc...

We describe a matrix multiply based block unsymmetric inverse iteration solver for upper Hessenberg matrices. Our kernel is robust in that it prevents overrow by scaling. It uses new techniques to ensure performance is not sacriiced when scaling is not necessary. Finally, we give results on a parallel implementation on an Intel Paragon TM supercomputer.

For the nonlinear eigenvalue problem T (λ)x = 0 we consider a Jacobi–Davidson type iterative projection method. The resulting projected nonlinear eigenvalue problems are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.

Non-symmetric and symmetric twisted block factorizations of block tridiagonal matrices are discussed. In contrast to non-blocked factorizations of this type, localized pivoting strategies can be integrated which improves numerical stability without causing any extra fill-in. Moreover, the application of such factorizations for approximating an eigenvector of a block tridiagonal matrix, given an...

This thesis focuses on designing robust and efficient algorithms for a class of matrix norm approximation (MNA) problems that are to find an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, network, control, engineering and other areas, such as finding the...

Inverse Iteration is widely used to compute the eigenvectors of a matrix once accurate eigenvalues are known. We discuss various issues involved in any implementation of inverse iteration for real, symmetric matrices. Current implementations resort to reorthogonalization when eigenvalues agree to more than three digits relative to the norm. Such reorthogonalization can have unexpected consequen...

This paper develops an inverse reinforcement learning algorithm aimed at recovering a reward function from the observed actions of an agent. We introduce a strategy to flexibly handle different types of actions with two approximations of the Bellman Optimality Equation, and a Bellman Gradient Iteration method to compute the gradient of the Qvalue with respect to the reward function. These metho...

The preconditioned inverse iteration [Ney01a] is an efficient method to compute the smallest eigenpair of a symmetric positive definite matrix M . Here we use this method to find the smallest eigenvalues of a hierarchical matrix [Hac99]. The storage complexity of the datasparse H-matrices is almost linear. We use H-arithmetic to precondition with an approximate inverse of M or an approximate Ch...

The conjugate gradient method applied to the normal equations (cgne) is known as one of the most efficient methods for the solution of (non-symmetric) linear equations. By stopping the iteration according to a discrepancy principle, cgne can be turned into a regularization method. We show that cgne can be accelerated by preconditioning in Hilbert scales, derive (optimal) convergence rates with ...