Multilevel matrix multiplication and fast solution of integral equations
Journal of Computational Physics
Multilevel Evaluation of Integral Transforms with Asymptotically Smooth Kernels
SIAM Journal on Scientific Computing
N Roots of the Secular Equation in O(N) Operations
SIAM Journal on Matrix Analysis and Applications
Recent developments of the Sinc numerical methods
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Fast convolution with radial kernels at nonequispaced knots
Numerische Mathematik
Wireless Technologies: Circuits, Systems, and Devices
Wireless Technologies: Circuits, Systems, and Devices
Handbook of Sinc Numerical Methods
Handbook of Sinc Numerical Methods
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A fast multilevel algorithm (MuST) for evaluating an $n$-sample sinc interpolant at $mn$ points is presented. For uniform grids, its complexity is $25mn\log(1/\delta)$ flops for the sinc kernel and $75mn\log(1/\delta)$ for the sincd kernel, where $\delta$ is the target evaluation accuracy. MuST is faster than FFT- and FMM-based evaluations for large $n$ and/or for large $\delta$. It is also applicable to nonuniform grids and to other kernels. Numerical experiments demonstrating the algorithm's practicality are presented.