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...

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...

We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left-and right-hand sides of rewrite rules, but introduce the notion of dependency pairs to compare left-hand sides with special subterms of the right-hand sides. This results in a technique which allows to apply existing methods for...

In a previous paper, the authors showed that the information complexity of the Fredholm problem of the second kind is essentially the same as that of the approximation problems over the spaces of kernels and right-hand sides. This allowed us to give necessary and sufficient conditions for the Fredholm problem to exhibit a particular level of tractability (for information complexity) over weight...

We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be saved and recombined through the eigenvectors of the tridiagonal projection matrix, which is equivalent theoretically to unrestarted Lanczos. Our algorithm capit...

In a wide number of applications in computational science and engineering the solution of large linear systems of equations with several right-hand sides given at once is required. Direct methods based on Gaussian elimination are known to be especially appealing in that setting. Nevertheless when the dimension of the problem is very large, preconditioned block Krylov space solvers are often con...

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial residuals must be collinear and this collinearity must be maintained at restart. Thus we cannot simultaneously solve shifted systems with unrelated right-hand si...

We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting.

We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.

We derive a differential inclusion governing the evolution of optimal trajectories to the Mayer problem. The value function is allowed to be discontinuous. This inclusion has convex compact right-hand sides.