The mass matrix for Gauss-Lobatto grid points is usually approximated by GaussLobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix and its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in O...

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...

  Introduction: Ordered subset expectation maximization (OSEM), is an effective iterative method for SPECT image reconstruction. The aim of this study is the evaluation of the role of system matrix in OSEM image reconstruction method using four different physical beam radiation models with three detection configurations. Methods: SPECT was done with an arc of 180 deg...

The concept of an inverse of a singular matrix seems to have been first introduced by Moore [1], [2] in 1920. Extensions of these ideas to general operators have been made by Tseng [3], [4], [5], but no systematic study of the subject was made until 1955 when Penrose [6], [7], unaware of the earlier work, redefined the Moore inverse in a slightly different way. About the same time one of the au...

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvec...

We introduce the concept of sandwich set of two fuzzy matrices.By using the new concept of sandwich set, we provide a method for finding a semi inverse of max-min product of fuzzy matrices. 1. Introduction Generalized inverse of matrices and its applications are studied by Rao and Mitra[3]. Ren et.al[4] introduced the concept of sandwich sets of matrices. By using the sandwich sets of matrices,...

Recently, a classi cation of matrices of class Z was introduced by Fiedler and Markham. This classi cation contains the classes ofM{matrices and the classes of N0 and F0{matrices studied by K. Fan, G. Johnson, and R. Smith. The problem of determining which nonsingular matrices have inverses which are Z{matrices is called the inverse Z{matrix problem. For special classes of Z{ matrices, such as ...

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly mod-eled, e.g. random-intercept, random-slope models. A Bayesian analysis of these problems requires a prior on the covariance matrix. Here we compare an inverse Wishart, scaled inverse Wishart, hierarchical inverse Wishart, and a sepa...

Two inverse eigenvalue problems are discussed. First, given the eigenvalues and a weight vector an extended Hessenberg matrix is computed. This matrix represents the recurrences linked to a (rational) Arnoldi inverse problem. It is well-known that the matrix capturing the recurrence coefficients is of Hessenberg form in the standard Arnoldi case. Considering, however, rational functions and adm...

We consider the problem of characterizing nonnegativity of the Moore-Penrose inverse for matrix perturbations of the type A − XGY, when the Moore-Penrose inverse of A is nonnegative. Here, we say that a matrix B = (b ij ) is nonnegative and denote it by B ≥ 0 if b ij ≥ 0, ∀i, j. This problemwasmotivated by the results in [1], where the authors consider an M-matrix A and find sufficient conditio...