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• W3016109905 startingPage "A1097" @default.
• W3016109905 abstract "This paper introduces a “kernel-independent” interpolative decomposition butterfly factorization (IDBF) as a data-sparse approximation for matrices that satisfy a complementary low-rank property. The IDBF can be constructed in $O(Nlog N)$ operations for an $Ntimes N$ matrix via hierarchical interpolative decompositions (IDs) if matrix entries can be sampled individually and each sample takes $O(1)$ operations. The resulting factorization is a product of $O(log N)$ sparse matrices, each with $O(N)$ nonzero entries. Hence, it can be applied to a vector rapidly in $O(Nlog N)$ operations. IDBF is a general framework for nearly optimal fast matrix-vector multiplication (matvec), which is useful in a wide range of applications, e.g., special function transformation, Fourier integral operators, and high-frequency wave computation. Numerical results are provided to demonstrate the effectiveness of the butterfly factorization and its construction algorithms." @default.
• W3016109905 created "2020-04-17" @default.
• W3016109905 creator A5018173193 @default.
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• W3016109905 date "2020-01-01" @default.
• W3016109905 modified "2023-09-23" @default.
• W3016109905 title "Interpolative Decomposition Butterfly Factorization" @default.
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• W3016109905 doi "https://doi.org/10.1137/19m1294873" @default.
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