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math.NA2021★ 5 cited
On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates
James Garritano, Yuval Kluger, Vladimir Rokhlin +1
In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A…
math.NA2021★ 1 cited
A Provably Componentwise Backward Stable QR Algorithm for the Diagonalization of Colleague Matrices
Kirill Serkh, Vladimir Rokhlin
The roots of a monic polynomial expressed in a Chebyshev basis are known to be the eigenvalues of the so-called colleague matrix, which is a Hessenberg matrix that is the sum of a…