Bayesian inverse problems with non-commuting operators

Inverse spectral problems for Sturm-Liouville operators with transmission conditions

Abstract: This paper deals with the boundary value problem involving the differential equation                      -y''+q(x)y=lambda y                                 subject to the standard boundary conditions along with the following discontinuity conditions at a point              y(a+0)=a1y(a-0),    y'(a+0)=a2y'(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Lio...

Functional Calculus for Non-Commuting Operators

Ela Polynomial Inequalities for Non-commuting Operators

We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.

Polynomial inequalities for non-commuting operators

Bayesian analysis in inverse problems

In this paper, we consider some statistical aspects of inverse problems. using Bayesian analysis, particularly estimation and hypothesis-testing questions for parameterdependent differential equations. We relate Bayesian maximum likelihood Io Tikhonw regularization. and we apply the expectatian-minimization (F-M) algorithm to the problem of setting regularization levels. Further, we compare Bay...