This paper is devoted to the study of some nonlinear hyperbolic equations or systems with discontinuous coefficients or with source terms. The common feature of the considered problems is the fact that the jacobian matrix of an associated autonomous system is not diagonalizable in R for many values of the unknown (leading to linear ill posed problems). However, the nonlinear problems appear to ...

The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. This paper discusses application of the GMRES method to the solution of large linear systems of equations that arise from the discretization of linear ill-posed problems. These linear systems are severely ill-conditioned and are referred to as discrete ill...

This paper presents direct settings and rigorous solutions of the main Statistical Inference problems. It shows that rigorous solutions require solving multidimensional Fredholm integral equations of the first kind in the situation where not only the right-hand side of the equation is an approximation, but the operator in the equation is also defined approximately. Using Stefanuyk-Vapnik theory...

The GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems variants of the standard GMRES method, that require the solution to live in the range ...

Let E, F ? Cnxn. If EFiE = 0 for all i N, we give the explicit representation of Drazin inverse block complex matrix (E I 0). We thereby solve a wider kind singular differential equations posed by Campbell [S.L. Campbell, The and systems second order linear equations, Linear & Multilinear Algebra, 14(1983), 195-198].

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the disturbing gravity observations are only available on the earth’s surface. downward contin...

abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...