Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

Calculation of Gauss quadrature rules.

Statistics For Spatial Data

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. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

http://sma.epfl.ch/~anchpcommon/publications/tensorsurvey.pdf

A literature survey of low-rank tensor approximation techniques

Studies in Advanced Mathematics

Nearly every numerical analysis algorithm has computational complexity that scales exponentially in the underlying physical dimension. The separated representation, introduced previously, allows many operations to be performed with scaling that is formally linear in the dimension. In this paper we further develop this representation by
(i) discussing the variety of mechanisms that allow it to be surprisingly efficient;
(ii) addressing the issue of conditioning;
(iii) presenting algorithms for solving linear systems within this framework; and 
(iv) demonstrating methods for dealing with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics.
Numerical examples are given.

/pdf/algorithms-for-numerical-analysis-in-high-dimensions-50uzif49bm.pdf

Algorithms for Numerical Analysis in High Dimensions

https://amath.colorado.edu/pub/wavelets/papers/BEY-MON-2005.pdf

On approximation of functions by exponential sums

https://amath.colorado.edu/faculty/beylkin/papers/BEY-MON-2010.pdf

Approximation by exponential sums revisited

https://amath.colorado.edu/pub/wavelets/papers/BEY-MON-2002.pdf

On Generalized Gaussian Quadratures for Exponentials and Their Applications

https://amath.colorado.edu/pub/wavelets/papers/BE-KU-MO-2009.pdf

Fast convolution with the free space Helmholtz Green's function

https://amath.colorado.edu/pub/wavelets/papers/MO-BE-HE-1999.pdf

Lucas Monzón

Papers

On approximation of functions by exponential sums

Approximation by exponential sums revisited

On Generalized Gaussian Quadratures for Exponentials and Their Applications

Fast convolution with the free space Helmholtz Green's function

Compactly Supported Wavelets Based on Almost Interpolating and Nearly Linear Phase Filters (Coiflets)