Design and Optimization of Numerical Methods for Solving Inverse Problems

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Numerical Methods for Solving Inverse Eigenvalue Problems for Nonnegative Matrices

Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomp...

Iterated Regularization Methods for Solving Inverse Problems

Numerical Methods for Inverse Singular Value Problems

Two numerical methods one continuous and the other discrete are proposed for solving inverse singular value problems The rst method consists of solving an ordinary di erential equation obtained from an explicit calculation of the projected gradient of a certain objective function The second method generalizes an iterative process proposed originally by Friedland et al for solving inverse eigenv...

Inexact Numerical Methods for Inverse Eigenvalue Problems

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...