Generalized Gaussian quadrature rules for systems of arbitrary functions
SIAM Journal on Numerical Analysis
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
Nonlinear Optimization, Quadrature, and Interpolation
SIAM Journal on Optimization
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Universal quadratures for boundary integral equations on two-dimensional domains with corners
Journal of Computational Physics
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
A Nyström method for weakly singular integral operators on surfaces
Journal of Computational Physics
Computing almost minimal formulas on the square
Journal of Computational and Applied Mathematics
A Bootstrap Method for Sum-of-Poles Approximations
Journal of Scientific Computing
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
On the numerical evaluation of the singular integrals of scattering theory
Journal of Computational Physics
A new Fast Multipole formulation for the elastodynamic half-space Green's tensor
Journal of Computational Physics
Journal of Computational Physics
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We present a new nonlinear optimization procedure for the computation of generalized Gaussian quadratures for a broad class of square integrable functions on intervals. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The new algorithm successfully computes generalized Gaussian quadratures in a number of instances in which the previous algorithms fail. Four applications of our scheme to computational physics are presented: the construction of discrete plane wave expansions for the Helmholtz Green's function, the design of linear array antennae, the computation of a quadrature for the discretization of Laplace boundary integral equations on certain domains with corners, and the construction of quadratures for the discretization of Laplace and Helmholtz boundary integral equations on smooth surfaces.