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Publications

Search Publications by Zydrunas Gimbutas

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Displaying 1 - 9 of 9

A fast simple algorithm for computing the potential of charges on a line

July 10, 2020
Author(s)
Zydrunas Gimbutas, Nicholas F. Marshall, Vladimir Rokhlin
We present a fast method for evaluating expressions of the form $$ u_j = \sum_{i = 1,i \not = j}^n \frac{\alpha_i}{x_i - x_j}, \quad \text{for} \quad j = 1,\ldots,n, $$ where $\alpha_i$ are real numbers, and $x_i$ are points in a compact interval of $

Evaluation of Abramowitz functions in the right half of the complex plane

March 15, 2020
Author(s)
Zydrunas Gimbutas, Shidong Jiang, Li-Shi Luo
A numerical scheme is developed for the evaluation of Abramowitz functions J n in the right half of the complex plane. For n = −1, . . . , 2, the scheme utilizes series expansions for |z| R with R determined by the required accuracy, and modified Laurent

Magnetic Resonance Imaging Biomarker Calibration Service: Proton Spin Relaxation Times

May 3, 2018
Author(s)
Michael A. Boss, Andrew M. Dienstfrey, Zydrunas Gimbutas, Kathryn E. Keenan, Jolene D. Splett, Karl F. Stupic, Stephen E. Russek
This document describes the calibration service to measure proton spin relaxation times, T1 and T2, of materials used in phantoms (calibration artifacts) to verify the accuracy of MRI-based quantitative measurements. Proton spin relaxation times are used

A Fast Summation Method for Oscillatory Lattice Sums

March 6, 2017
Author(s)
Ryan Denlinger, Leslie Greengard, Zydrunas Gimbutas, Vladimir Rokhlin
We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach

The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

May 28, 2015
Author(s)
Felipe Vico, Leslie Greengard, Miguel Ferrando, Zydrunas Gimbutas
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A, φ in the Lorenz gauge, we

Randomized methods for rank-deficient linear systems

February 13, 2015
Author(s)
Josef Sifuentes, Zydrunas Gimbutas, Leslie Greengard
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without additional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix