1,841 research outputs found
A literature survey of low-rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as
a new tool in scientific computing to address large-scale linear and
multilinear algebra problems, which would be intractable by classical
techniques. This survey attempts to give a literature overview of current
developments in this area, with an emphasis on function-related tensors
Fast Algorithms for the computation of Fourier Extensions of arbitrary length
Fourier series of smooth, non-periodic functions on are known to
exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of
overcoming these problems is by using a Fourier series on a larger domain, say
with , a technique called Fourier extension or Fourier
continuation. When constructed as the discrete least squares minimizer in
equidistant points, the Fourier extension has been shown shown to converge
geometrically in the truncation parameter . A fast algorithm has been described to compute Fourier extensions for the case
where , compared to for solving the dense discrete
least squares problem. We present two algorithms for
the computation of these approximations for the case of general , made
possible by exploiting the connection between Fourier extensions and Prolate
Spheroidal Wave theory. The first algorithm is based on the explicit
computation of so-called periodic discrete prolate spheroidal sequences, while
the second algorithm is purely algebraic and only implicitly based on the
theory
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