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:
“From a hasty glance through the various tests I figure it out that I would be classified in Group B, indicating “Low Average Ability,” reserved usually for those just learning to speak the English Language and preparing for a career of holding a spike while another man hits it.”
—Robert Benchley (1889–1945)
“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)
“The intellect is vagabond, and our system of education fosters restlessness. Our minds travel when our bodies are forced to stay at home. We imitate; and what is imitation but the travelling of the mind?”
—Ralph Waldo Emerson (1803–1882)