Digit Stability Inference for Iterative Methods Using Redundant Number Representation

In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for solution of problem at hand. Significant proportions these performance improvements stem from ability to infer existence identical most-significant digits between iterations. This technique uses properties algorithms operating redundantly represented numbers allow generation those be skipped, increasing efficiency. It is unable, however, guarantee will stabilize, i.e., never change any future iteration. this article, address shortcoming, using interval and forward error analyses prove high significance become stable computing approximants systems linear equations stationary methods. We formalize relationship matrix conditioning rate growth digit stability, information converge desired results quickly. Versus previous work, an exemplary hardware realization new achieves up-to 2.2× speedup a set variously conditioned Jacobi method.