Approximation of 1/x by exponential sums in [1, ∞)

By Dietrich Braess, Wolfgang Hackbusch. 2005

70 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ivan V. Oseledets
2. E. E. Tyrtyshnikov
3. Daniel Kressner
4. Christine Tobler
5. Boris N. Khoromskij
6. Dmitry V. Savostyanov

In Numerical Analysis

1. Ivan V. Oseledets
2. Daniel Kressner
3. Christine Tobler
4. E. E. Tyrtyshnikov
5. Martin Plesinger
6. Boris N. Khoromskij
7. Wolfgang Hackbusch
8. Dmitry V. Savostyanov

In Statistics and Probability

1. Christine Tobler
2. Daniel Kressner
3. Ivan V. Oseledets
4. E. E. Tyrtyshnikov
5. Martin Plesinger
6. Boris N. Khoromskij

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For this purpose, various approaches have been discussed in [27–29, 36, 37].”
• Approximation by exponential sums revisited (2010, unknown): “Approximation of 1/r by sum of exponentials has been also been studied in [35] and [20] [21].”
• Krylov Subspace Methods for Linear Systems with Tensor Product Structure (2010, unknown): “Lemma 2.6 ([6]).”
• Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems (2011, background): “Such approximations can be constructed by means of an exponential sum, see [9].”
• Use of tensor formats in elliptic eigenvalue problems (2012, unknown): “For its computation and analysis see [5, 12, 13, 16, 17, 29].”
• Variational calculus with sums of elementary tensors of fixed rank (2012, unknown): “In order to compare our results, we set rank(b) = R := 1 and also compute a separable approximation of the inverse of A with the use of exponential sums, see [4].”
• A preconditioned low‐rank CG method for parameter‐dependent Lyapunov matrix equations (2014, background): “Proof We start by recalling existing results [44, 4, 6] on the singular value decay of X(α) for fixed α ∈ [−1, 1].”
• Algorithm 941 (2014, background): “Suitable coefficients αj ,ωj are described in [10, 13].”
• TT-cross approximation for multidimensional arrays (2010, background): “The second example is the Hilbert tensor with elements For this kind of tensors it is known that a nice low-canonical-rank approximations exists (cf. [7]) and can be computed in various ways.”