Solving Generalized Small Inverse Problems

Solving Generalized Small Inverse Problems

We introduce a “generalized small inverse problem (GSIP)” and present an algorithm for solving this problem. GSIP is formulated as finding small solutions of f(x0, x1, . . . , xn) = x0h(x1, . . . , xn) + C = 0(mod M) for an n-variate polynomial h, non-zero integers C and M . Our algorithm is based on lattice-based Coppersmith technique. We provide a strategy for construction of a lattice basis ...

Solving Inverse Tomography Problems

1. Introduction. Inverse problems are encountered typically in situations where one makes indirect observations of a quantity of interest. Solving a inverse problem means determining the parameters of a model given a set of measurements. In solving practical inverse problems, accounting for the uncertainty of the solution is important in making decision. In this project, we explored an algorith...

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Generalized B-spline functions ‎method‎‎ for solving optimal control problems

‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs) ‎using collocation methods‎. ‎This approach is based upon B-spline functions‎. ‎The derivative matrices between any two families of B-spline functions are utilized to‎ ‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎. ‎Numerical experiments confirm our heoretical findings‎.

Iterated Regularization Methods for Solving Inverse Problems