SPIKE As A Polyalgorithmic Banded Linear System Solver
Despite being logically divided into two stages, computationally, the SPIKE algorithm comprises three stages:
- factorizing the diagonal blocks,
- computing the spikes,
- solving the reduced system.
Each of these stages can be accomplished in several ways, allowing a multitude of variants. Two notable variants are the recursive SPIKE algorithm for non-diagonally-dominant cases and the truncated SPIKE algorithm for diagonally-dominant cases. Depending on the variant, a system can be solved either exactly or approximately. In the latter case, SPIKE is used as a preconditioner for iterative schemes like Krylov subspace methods and iterative refinement.
Read more about this topic: SPIKE Algorithm
Famous quotes containing the words spike, banded and/or system:
“Directors like Satyajit Ray, Rossellini, Bresson, Buñuel, Forman, Scorsese, and Spike Lee have used non-professional actors precisely in order that the people we see on the screen may be scarcely more explained than reality itself. Professionals, except fo the greatest, usually play not just the necessary role, but an explanation of the role.”
—John Berger (b. 1926)
“That excitement about Kossuth, consider how characteristic, but superficial, it was!—only another kind of politics or dancing. Men were making speeches to him all over the country, but each expressed only the thought, or the want of thought, of the multitude. No man stood on truth. They were merely banded together, as usual one leaning on another, and all together on nothing.”
—Henry David Thoreau (1817–1862)
“Every political system is an accumulation of habits, customs, prejudices, and principles that have survived a long process of trial and error and of ceaseless response to changing circumstances. If the system works well on the whole, it is a lucky accident—the luckiest, indeed, that can befall a society.”
—Edward C. Banfield (b. 1916)