Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing


  • March 29, 2007
  • 11:00 am - 11:25 am

A residual inverse power method

Pete Stewart (University of Maryland)

The inverse power method involves solving shifted equations of the form (A -σ I)v = u. This talk describes a variant method in which shifted equations may be solved to a fixed reduced accuracy without affecting convergence. The idea is to alter the right-hand side to produce a correction step to be added to the current approximations. The digits of this step divide into two parts: leading digits that correct the solution and trailing garbage. Hence the step can be be evaluated to a reduced accuracy corresponding to the correcting digits. The cost is an additional multiplication by A at each step to generate the right-hand side. Analysis and experiments show that the method is suitable for normal and mildly nonnormal problems.

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