in this paper, an iterative method is proposed for solving the matrix inverse problem $ax=b$ for hermitian-generalized hamiltonian matrices with a submatrix constraint. by this iterative method, for any initial matrix $a_0$, a solution $a^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...

We consider here a classical problem of estimating or approximating a density given the information consisting of the values of some of its integrals. The method will have direct applications in many problems of density, spectral density and image analysis which will not be treated in any detail here. One widely used method chooses the density which minimizes a cross entropy functional. We prop...

In this paper, we propose an algorithm for numerical solving an inverse nonlinear diffusion problem. The algorithm is based on the linearized nonlinear terms by Taylor ́s series expansion, removed the time-dependent terms by Laplace transform, and so, the results at a specific time can be calculated without step-by-step computations in the time domain. Finite difference technique used for discre...

We formulate the inverse problem of solving Fredholm integral equations of the first kind as a nonparametric Bayesian inference problem, using Lévy random fields (and their mixtures) as prior distributions. Posterior distributions for all featues of interest are computed using novel Markov chain Monte Carlo numerical methods in infinite-dimensional spaces, based on generalizations and extension...

A new algorithm is proposed for solving the inverse Sturm–Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov’s method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorith...

A partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized K-centrohermitian matrices are considered. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solution of the inverse eigenproblem exists, the optimal approximation problem can be solved. The formula o...