ﻻ يوجد ملخص باللغة العربية
Polynomial preconditioning with the GMRES minimal residual polynomial has the potential to greatly reduce orthogonalization costs, making it useful for communication reduction. We implement polynomial preconditioning in the Belos package from Trilinos and show how it can be effective in both serial and parallel implementations. We further show it is a communication-avoiding technique and is a viable option to CA-GMRES for large-scale parallel computing.
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial and is straightforward to compute and implement. It this paper, we study the polynomial preconditione
Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector p
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of reverse reduced basis of linearly independent polynomials and design an algorithm
We analyze the the convergence behavior of block GMRES and characterize the phenomenon of stagnation which is then related to the behavior of the block FOM method. We generalize the block FOM method to generate well-defined approximations in the case
The programming paradigm Map-Reduce and its main open-source implementation, Hadoop, have had an enormous impact on large scale data processing. Our goal in this expository writeup is two-fold: first, we want to present some complexity measures that