An algorithm is presented for constructing an approximate numerical solution to a large scale Lyapunov equation in low rank factored form. The algorithm is based upon a synthesis of an approximate power method and an alternating direction implicit (ADI) method. The former is parameter free and tends to be efficient in practice, but there is little theoretical understanding of its convergence pr...

The main goal of the paper is to approximate two types inverse problems for conformable heat equation (or called parabolic with operator); as follows, we considered cases: right hand side such that F x , t and id="M2"> = φ...

In the theory of inverse systems, in order to study the properties of a space X or a map f : X → Y between spaces, one expands X to an inverse system X or expands f to a map f : X → Y between the inverse systems, and then work on X or f . In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f : X → Y between compact metric spaces is in...

Focusing is traditionally seen as a means of reducing inessential nondeterminism in backward-reasoning strategies such as uniform proof-search or tableaux systems. In this paper we construct a form of focused derivations for propositional linear logic that is appropriate for forward reasoning in the inverse method. We show that the focused inverse method conservatively generalizes the classical...

The " LHC Inverse Problem " refers to the question of determining the underlying physical theory giving rise to the signals expected to be seen at the Large Hadron Collider. The solution to this problem (Bard) is reviewed. The combination of CDF and DØ data is motivated. These proceedings explore the incorrectness of each of the three words in " LHC Inverse Problem. " We work backward. Sections...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

Abstract A method for computing an approximate inverse preconditioner of a matrix A which all eigenvalues have negative real parts is proposed. The approximate solution of the special Sylvester matrix equation AX+ XA = I, which is an approximate inverse preconditioner of matrix A, is obtaining by the successive approximations method. Some numerical experiments on test matrices from Harwell-Boin...

Modal logic represents knowledge that agents have about other agents’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competitions. Unfortunately, probabilistic modal structures are impractical for large real-world applicat...