GMRES is a popular iterative method for the solution of linear system of equations with an unsymmetric square matrix. Range restricted GMRES (RRGMRES) is one GMRES version proposed by Calvetti et al in 2000. In this paper, a weighted implementation for RRGMRES is proposed. Numerical results prove this weighted RRGMRES is better than RRGMRES.

A finite latin square is an n × n matrix whose entries are elements of the set {1, . . . , n} and no element is repeated in any row or column. Given equivalence relations on the set of rows, the set of columns, and the set of symbols, respectively, we can use these relations to identify equivalent rows, columns and symbols, and obtain an amalgamated latin square. There is a set of natural equat...

In this article the new method for the accounting singular point influence to the postprocessing error estimation is proposed. Solution improvement in singular zones is achieved modifying physical coordinate matrix used in least square problem equations: instead of the standard quadratic polynomial a new polynomial with singular elements is taken. Numerical examples demonstrate the advantages o...

We review basics on least square problems. The material is mainly taken from books [2, 1, 3]. We consider an overdetermined system Ax = b where Am×n is a tall matrix, i.e., m > n. We have more equations than unknowns and in general cannot solve it exactly.

Release properties from a wax matrix tablet was examined. To obtain basic release properties, the wax matrix tablet was prepared from a physical mixture of drug and wax powder (hydrogenated caster oil) at a fixed mixing ratio. Properties of release from the single flat-faced surface or curved side surface of the wax matrix tablet were examined. The applicability of the square-root time law and ...

We consider the real ε-pseudospectrum of a real square matrix, which is the set of eigenvalues of all real matrices that are ε-close to the given matrix, where closeness is measured in either the 2-norm or the Frobenius norm. We characterize extremal points and compare the situation with that for the complex ε-pseudospectrum. We present differential equations for rank-1 and rank2 matrices for t...

this research presents a numerical tool to estimate the green's function operator matrix of intraplate faults. having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. this information could be employed to predict the location of future powerful earthquakes. to implement fault sliding in fe calculations,...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...