HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems

Mixed cell computation in Hom4PS-3

Global sensitivity analysis using sparse grid interpolation and polynomial chaos

Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evalua...

Solving Polynomial Systems Symbolically and in Parallel

We discuss the parallelization of algorithms for solving polynomial systems symbolically. We introduce a component-level parallelization: our objective is to develop a parallel solver for which the number of processors in use depends on the intrinsic complexity of the input system, that is on geometry of its solution set. This approach creates new opportunities for parallel execution of polynom...

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

Parallel computation of real solving bivariate polynomial systems by zero-matching method

We present a new algorithm for solving the real roots of a bivariate polynomial system R 1⁄4 ff ðx; yÞ; gðx; yÞg with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for the bivariate polynomial system when the system is non-zero. Moreover, the multiplicities of the roots of R 1⁄4 0 can be obtained by the associated quotient ring technique and ...