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3.2 CSI-MSVD for the Matrix

  The SVD of the matrix A may also be obtained from the eigenvalue decomposition of the matrix . When , the matrix is considerably smaller than the corresponding two-cyclic matrix C of Equation (2). The CSI-MSVD algorithm could be applied to approximate the eigenvalues and eigenvectors of . However, the simplifications possible for the two-cyclic matrix may not be applied to this case. For example, it is not possible to re-write Equation (11) by partitioning the iterates to obtain two dependent iterations as was done to obtain Equations (26) and (27). Also, the simplification provided by Equation (29) does not apply in this case. Other disadvantages arising from iterates generated by the matrix are discussed in [22].

Michael W. Berry (
Sun May 19 11:34:27 EDT 1996