Computation of Pseudo-Differential Operators
Gang Bao,William W. Symes +1 more
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TLDR
A simple algorithm is described for computing general pseudo-differential operator actions based on the asymptotic expansion of the symbol together with the fast Fourier transform, which shows that the algorithm is efficient through analyzing its complexity.Abstract:
A simple algorithm is described for computing general pseudo-differential operator actions. Our approach is based on the asymptotic expansion of the symbol together with the fast Fourier transform (FFT). The idea is motivated by the characterization of the pseudo-differential operator algebra. We show that the algorithm is efficient through analyzing its complexity. Some numerical experiments are also presented.read more
Citations
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A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
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An approximate inverse to the extended Born modeling operator
Jie Hou,William W. Symes +1 more
TL;DR: In this paper, the authors modified RTM in the subsurface offset domain to create an asymptotic (high-frequency) approximation to extended Born inversion operator.
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Fast Computation of Fourier Integral Operators
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Fast Computation of Fourier Integral Operators
TL;DR: A new numerical algorithm which requires O(N^{2.5} \log N) operations and as low as $O(\sqrt{N})$ in storage space (the constants in front of these estimates are small).
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Accelerating extended least-squares migration with weighted conjugate gradient iteration
Jie Hou,William W. Symes +1 more
TL;DR: In this article, the convergence of extended least-squares migration is accelerated by combining the conjugate gradient algorithm with weighted norms in range (data) and domain (model) spaces that render the extended Born modeling operator approximately unitary.
References
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Book
Computational Frameworks for the Fast Fourier Transform
TL;DR: The Radix-2 Frameworks, a collection of general and high performance FFTs designed to solve the multi-Dimensional FFT problem of Prime Factor and Convolution, are presented.