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- W2070868049 abstract "In this paper, we improve the algorithms for the construction of the wavelet-like basis matrix introduced by Alpert et al. [1]. It has been shown in [1] that the n × n wavelet-like basis matrix is of the form U = U l U l −1 … U 1 , where n = k 2 l is the number of quadrature points and U j , j = 1…, l are sparse orthogonal matrices. In this paper, we prove that each U j (1 ≤ j ≤ l ) can be represented by a 2 k × 2 k matrix. It follows that the storage requirement for all matrices U j is 4 lk 2 . We also show that the cost of the construction of all matrices U j can be reduced to O ( lk 3 ) = O (log n · k 3 ). We recall that in [1], the storage requirement and the construction cost of the matrix U are 4 nk and O ( nk 2 ), respectively." @default.
- W2070868049 created "2016-06-24" @default.
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- W2070868049 date "2000-09-01" @default.
- W2070868049 modified "2023-09-28" @default.
- W2070868049 title "Notes on wavelet-like basis matrices" @default.
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- W2070868049 doi "https://doi.org/10.1016/s0898-1221(00)00194-2" @default.
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