Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Generalized Gaussian quadrature rules for systems of arbitrary functions
SIAM Journal on Numerical Analysis
A Fast Adaptive Numerical Method for Stiff Two-Point Boundary Value Problems
SIAM Journal on Scientific Computing
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
SIAM Journal on Numerical Analysis
Fast Convolution for Nonreflecting Boundary Conditions
SIAM Journal on Scientific Computing
Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
On the numerical inversion of the Laplace transform of certain holomorphic mappings
Applied Numerical Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Fast and Oblivious Convolution Quadrature
SIAM Journal on Scientific Computing
A Spectral Order Method for Inverting Sectorial Laplace Transforms
SIAM Journal on Numerical Analysis
Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
SIAM Journal on Scientific Computing
A Fast Time Stepping Method for Evaluating Fractional Integrals
SIAM Journal on Scientific Computing
A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
SIAM Journal on Scientific Computing
Incorporating the Havriliak-Negami dielectric model in the FD-TD method
Journal of Computational Physics
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A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138---1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples.