After tersely reviewing the various meanings that can be given to property of a system nonlinear ODEs solvable, we identify special case two first-order with homogeneous quadratic right-hand sides which is explicitly solvable. It identified by 2 explicit algebraic constraints on 6 priori arbitrary parameters characterize this system. Simple extensions model cases nonhomogeneous are also identif...

This paper looks at the iterative solution of complex, non-Hermitian systems of linear equations associated with a lattice QCD problem in particle physics. Let the n by n system of equations be Ax = b. We use a version of the GMRES method that deflates eigenvalues and can solve systems with multiple right-hand sides. We give examples that show deflating eigenvalues can make a significant improv...

The knowledge integration problem arises in rule-based expert systems when two or more recommendations made by right-hand sides of rules must be combined. Current expert systems address this problem either by engineering the rule set to avoid it, or by using a single integration technique built into the interpreter, e.g., certainty factor combination. We argue that multiple techniques are neede...

We propose a variant of the block GMRES method for the solution of linear systems of equations with multiple right-hand sides. We investigate a deflation strategy to detect when a linear combination of approximate solutions is already known that avoids performing expensive computational operations with the system matrix. We specifically focus on the block GMRES method incorporating deflation at...

Level-confluence is an important property of conditional term rewriting systems that allow extra variables in the rewrite rules because it guarantees the completeness of narrowing for such systems. In this paper we present a syntactic condition ensuring level-confluence for orthogonal, not necessarily terminating, conditional term rewriting systems that have extra variables in the right-hand si...

We consider probabilistically constrained problems, in which the multivariate random variables are located in the right-hand sides. The objective function is linear, and its optimization is subject to a set of linear constraints as well as a joint probabilistic constraint enforcing that the joint fulfillment of a system of linear inequalities with random right-hand side variables be above a pre...

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nyström method is applied to the regularized equation. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The spe...

A Toeplitz matrix has constant diagonals; a multilevel Toeplitz matrix is defined recursively with respect to the levels by replacing the matrix elements with Toeplitz blocks. Multilevel Toeplitz linear systems appear in a wide range of applications in science and engineering. This paper discusses an MPI implementation for solving such a linear system by using the conjugate gradient algorithm. ...

Contemporary applications in computational science and engineering often require the solution of linear systems which may be different sizes, shapes, structures. The goal this paper is to explain how two libraries, PETSc HPDDM, have been interfaced order offer end-users robust overlapping Schwarz preconditioners advanced Krylov methods featuring recycling ability deal with multiple right-hand s...

The explicit solution x n t , $x_{n}\left (t\right ) ,$ = 1,2, of the initial-values problem is exhibited a subclass autonomous system 2 coupled first-order ODEs with second-degree polynomial right-hand sides, hence featuring 12 priori arbitrary (time-independent) coefficients: ̇ c 1 + 3 4 5 6 . $$ \dot{x}_{n}=c_{n1}\left( x_{1}\right)^{2}+c_{n2}x_{1}x_{2}+c_{n3}\left( x_{2}\right)^{2}+c_{n4}x_{...