Romberg integration using systolic arrays (Q1820548)

Because of its special shape, the triangular Richardson extrapolation scheme, especially the Romberg integration scheme, is suitable for the use of systolic arrays. The scheme is constructed diagonally. The first column \(R_{i,1}\) is executed in a host computer while the extrapolated values \(R_{ij}\), \(i=2(1)n\), \(j=2(1)i\), are to be obtained in n-1 REP- cells (REP from Richardson extrapolation procedure). The time needed for computation of a full scheme with n entries behaves like 3n-3 which improves the usual \(O(n^ 2)\) essentially. The paper contains the program listing and an illustrating example.