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Fast algorithm for matrix–vector multiply of asymmetric multilevel block‐Toeplitz matrices in 3‐D scattering
Author(s) -
Barrowes Benjamin E.,
Teixeira Fernando L.,
Kong Jin A.
Publication year - 2001
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.1348
Subject(s) - toeplitz matrix , matrix (chemical analysis) , block (permutation group theory) , algorithm , fast fourier transform , mathematics , convergence (economics) , microwave , block matrix , combinatorics , physics , pure mathematics , materials science , eigenvalues and eigenvectors , quantum mechanics , economics , composite material , economic growth
A new O ( N log N ) FFT‐based method to expedite matrix–vector multiplies involving multilevel block‐Toeplitz (MBT) matrices is presented. The method is also a minimal memory method with O ( N ) memory requirements because only nonredundant entries of the MBT matrix are stored. The accuracy and convergence of the method are illustrated in the calculation of the scattered field and the effective permittivity of a sphere with size parameter ka up to 5 using a volume integral formulation akin to the discrete dipole approximation. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 28–32, 2001.