The solution $x_n\left(t\right)$, $n=1,2,$ of the \textit{initial-values} problem is reported \textit{autonomous} system $2$ coupled first-order ODEs with \textit{homogeneous cubic polynomial} right-hand sides, \begin{eqnarray} \dot{x}_n = c_{n1} \left(x_1\right)^3 + c_{n2}\left( x_1\right)^2 x_2 c_{n3} x_1 \left(x_2\right)^2+c_{n4} \left(x_2\right)^3\ ,\quad n=1,2\ , \nonumber \end{eqnarray} w...

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set points. The boundaries themselves may be non-smooth. scheme, which builds on recursively compressed inverse preconditioning (RCIP), universal as it independent nature singularities. Strong right-hand-side singularities, such 1/|r|α α close ...

The reduction of a large-scale symmetric linear discrete ill-posed problem with multiple right-hand sides to smaller block tridiagonal matrix can easily be carried out by the application small number steps Lanczos method. We show that subdiagonal blocks reduced converge zero fairly rapidly increasing number. This quick convergence indicates there is little advantage in expressing solutions prob...

This paper discusses an Interval Quadratic Programming (IQP) problem, where the constraints coefficients and the right-hand sides are represented by interval data. First, the focus is on a common method for solving Interval Linear Programming problem. Then the idea is extended to the IQP problem. Based on this method each IQP problem is reduced to two classical Quadratic Programming (QP) proble...

In this work an algorithm for solving triangular systems of equations for multiple right hand sides is presented. The algorithm for solving triangular systems for multiple right hand sides, commonly referred to as the TRSM problem, is a very important in dense linear algebra as it is a subroutine for most decompositions of matrices as LU or QR. To improve performance over the standard iterative...

Existing definitions of componentwise backward error and componentwise condi tion number for linear systems are extended to systems with multiple right-hand sides and to a general class of componentwise measure of perturbations involving Holder p-norms. It is shown that for a system of order n with r right-hand sides, the componentwise backward error can be computed by finding the minimum p-nor...

In this paper we address the solution of linear systems of equations with multiple right-hand sides given at once. When the dimension of the problem is known to be large, preconditioned block Krylov subspace methods are usually considered as the method of choice. Nevertheless to be effective in terms of computational operations it is known that these methods must incorporate a strategy for dete...

Abstract In classical texts, equations for fields are proposed without derivation of right-hand sides. Below, the sides Maxwell and Einstein derived within framework Vlasov–Maxwell–Einstein from a classical, but slightly more general principle least action Hamilton–Jacobi used to obtain cosmological solutions.