Two-dimensional systolic array for the column-by-column QD algorithm

A 2D systolic array for the column-by-column QD algorithm is presented. The design requires 4n+R+S-4 steps and (n-1)(2n+2R-1) processors to compute at least R iterations to the roots of S polynomials of degree less than or equal to n. A proof of correctness is given to verify the design and it is shown that the array is asymptotically optimal with respect to processor and bandwidth utilisation. Various extensions to the array are also discussed; in particular it is shown that a rectangular array of O(n²) processors (i.e. independent of R) can be used to produce an unlimited number of iterations.