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...

In this paper we consider the problem of locating a small three-dimensional elastic inclusion, using arrays of elastic source transmitters and receivers. This procedure yields the multi-static response matrix that is characteristic of the elastic inclusion. We show how the eigenvalue structure of this matrix can be employed within the framework of a non-iterative method of MUSIC (standing for M...

This paper presents a parallel mixed direct/iterative method for solving linear systems Ax = b arising from circuit simulation. The systems are solved by a block LU factorization with an iterative method for the Schur complement. The Schur complement is a small and rather dense matrix. Direct LU decomposition of the Schur complement takes too much time in order to achieve reasonable speedup res...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...