Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz atrices

We describe a new fast Fourier transform (FFT)-based algorithm to expedite matrix-vector multiplies involving multilevel block-Toeplitz (BT), or T/sub f/ /sup M/ matrices. Matrices of this class often occur in electromagnetic scattering applications because of the convolutional nature of the Green's function. Multilevel BT matrices are also associated with the autocorrelation of a 2-D discrete random process and with many problems involving symmetries based on cubic meshes. The algorithm presented here applies to multilevel BT matrices with blocks and sub-blocks which are themselves BT and in general asymmetric. The algorithm also provides for the last, M/sup th/ level sub-block to be a square, dense, not necessarily Toeplitz matrix. This method has a similar purpose to that of Goodman, Draine and Flatau (1991), but uses less memory and is more general in implementation.