Purpose: The inverse of a deformation vector field (DVF) is often needed in deformable registration, 4D image reconstruction, and adaptive radiation therapy. This study aims at improving both accuracy with respect to inverse consistency and efficiency for numerical DVF inversion, by the development of a fixed-point iteration method with feedback control. Method: We introduce an iterative method...

A complete characterization of the convergence factor can be very useful when analyzing the asymptotic convergence of an iterative method. We will here establish a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well known inverse iteration. The formula for the convergence factor ...

In this letter, we propose a novel iterative method for computing generalized inverse, based on a novel KKT formulation. The proposed iterative algorithm requires making four matrix and vector multiplications at each iteration and thus has low computational complexity. The proposed method is proved to be globally convergent without any condition. Furthermore, for fast computing generalized inve...

Two-norm normalized inverse, shifted inverse, and Rayleigh quotient iteration are well-known algorithms for approximating an eigenvector of a symmetric matrix. In this work we establish rigorously that each one of these three algorithms can be viewed as a standard form of Newton’s method from the nonlinear programming literature, followed by the normalization. This equivalence adds considerable...