Inverse iteration is a standard technique for nding selected eigenvectors associated with eigenvalues which are known approximately. At each step the solution of a linear system of equations is required, which is usually done by factorizing the system matrix. When direct factorization is impractical, iterative methods can be applied for solving the linear systems. Several results about terminat...

In this paper, we survey some of the latest development in using inexact Newton-like methods for solving inverse eigenvalue problems. These methods require the solutions of nonsymmetric and large linear systems. One can solve the approximate Jacobian equation by iterative methods. However, iterative methods usually oversolve the problem in the sense that they require far more (inner) iterations...

Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on position or pose one more end-effectors. For robots with redundant degrees freedom, there often an infinite, nonconvex set solutions. The IK further complicated when collision avoidance are imposed by obstacles in workspace. In general, closed-form expressions yielding feasible do not exist,...

We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.

We interprete non-overlapping domain decomposition methods as multiplicative subspace correction algorithms in the framework of Xu [8]. This allows us to estimate the effects of the perturbation which is created by an inexact solution of the problems on the subdomains that must be solved in each iteration. The general results are applied to finite element discretizations of the Poisson and Stok...

In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau–Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer ite...

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how material and radiation energy coupled, which determines number of iterations needed to converge emission source, diffusion equation is solved, must be done each iteration. The coupled equations solved using an inexact Newton it...