Vico-Greengard-Ferrando quadratures in the tensor solver for integral\n equations

2017/04/05 by Valentin Khrulkov, Khrulkov, Valentin, Maxim Rakhuba +3
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1704.01669

openalex publication_date 2017/04/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Convolution with Green's function of a differential operator appears in a lot\nof applications e.g. Lippmann-Schwinger integral equation. Algorithms for\ncomputing such are usually non-trivial and require non-uniform mesh. However,\nrecently Vico, Greengard and Ferrando developed method for computing\nconvolution with smooth functions with compact support with spectral accuracy,\nrequiring nothing more than Fast Fourier Transform (FFT). Their approach is\nvery suitable for the low-rank tensor implementation which we develop using\nQuantized Tensor Train (QTT) decomposition.\n

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