We give a systolic algorithm and array for bidiagonalization of an n x n matrix in O(nlog, n) time, using O(n2) ' + n) cells are needed. This is faster than the best previously reported result by the factor log, e = 1.44.. .. Moreover, in contrast to earlier systolic designs, which require the matrix to be preloaded into the array and the result matrix extracted after bidiagonalization, the present arrays are pipelined.
Work reported herein
AbstractWe give a systolic algorithm and array for bidiagonalization of an n x n matrix in O ( n log, n) time, using O(nZ) cells. Bandedness of the input matrix may be effectively exploited. If the matrix is banded, with p nonzero subdiagonals and q nonzero superdiagonals, then 4n In(p + q) + O(n) clocks aad 2n(p -+ q ) + O( ( p + q)2 + n) cells are needed. This is faster than the best previously reported result by the factor log, e = 2-44 -0 . Moreover, in contrast to earlier systolic designs, which require the matrix to be preloaded into the array and the result matrix extracted after bidiagonaiization, the present arrays are pipelind