Systolic designs for Aitken's root finding method

Abstract

1-D and 2-D systolic arrays for computing the roots of a transcendental function via table generating methods are considered. In particular we show how to derive systolic arrays systematically for a problem with an unbounded computation domain. A non-linear scheduling function is introduced to partition the domain into finite-sized blocks and normal synthesis techniques used to derive block arrays. A m × n block can be computed in at most 3n + m − 1 steps using O(n) cells in a 1-D array and O(mn + n2) cells in a 2-D array. Different problem instances can be pipelined in the latter and the whole table can be produced by using the arrays iteratively.