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Fixed-Point Lanczos with Analytical Variable Bounds

Author(s):

J.L. Jerez
Conference/Journal:

SIAMLA - Conference on Applied Linear Algebra, Valencia, Spain
Abstract:

We consider the problem of establishing analytical bounds on all variables calculated during the symmetric Lanczos process with the objective of enabling fixed-point im- plementations with no overflow. Current techniques fail to provide practical bounds for nonlinear recursive algorithms. We employ a diagonal preconditioner to control the range of all variables, regardless of the condition number of the original matrix. Linear algebra techniques are used to prove the proposed bounds. It is shown that the result- ing fixed-point implementations can lead to similar numerical behaviour as with double precision floating-point while providing very significant performance improvements in custom hardware implementations.

Year:

2012
Type of Publication:

(06)Talk
Supervisor:



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