A Proof of Convergence for Two Parallel Jacobi SVD Algorithms
IEEE Transactions on Computers
A singular value decomposition updating algorithm for subspace tracking
SIAM Journal on Matrix Analysis and Applications
A systolic array for SVD updating
SIAM Journal on Matrix Analysis and Applications
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Given the matrix A Ɛ Cn×n and scalars λ1, λ2, ...., λm Ɛ C, our task is to design a systolic implementation of the matrix portrait computation - i.e., the singular value decomposition of matrices A - λkI; k = 1, 2, ..., m. We propose the triangular-rectangular and hexagonal systolic subarrays for the recursive QR updating of matrices A - λkI, and another triangular subarray for the singular value decomposition of the R-factor. Let m, n and r be the number of various λs, the matrix order and the number of repeated loops in the SVD algorithm, respectively. Due to the large amount of overlap between subarrays, the time complexity of our solution is O(3mn) whereas the straightforward systolic implementation requires O(⌈7/2mn⌈+4rm) times steps. The number of PEs and delays is O(⌈cn2⌈), where c = 37/8 for our solution and c = 5/8 for the straight forward solution.