1 citations · 1 across the 4 of their papers we have counts for
4 papers
Conditioning of solutions to the Sylvester equation
Massimiliano Fasi, Behnam Hashemi
We partially answer an open problem, posed by Nick Higham, concerning the conditioning of solutions to Sylvester and Lyapunov equations. The question arises in the backward stabili…
The Laurent-Horner method for validated evaluation of Chebyshev expansions
Jared L. Aurentz, Behnam Hashemi
We develop a simple two-step algorithm for enclosing Chebyshev expansions whose cost is linear in terms of the polynomial degree. The algorithm first transforms the expansion from…
Rectangular eigenvalue problems
Behnam Hashemi, Yuji Nakatsukasa, Lloyd N. Trefethen
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation po…
Least-squares spectral methods for ODE eigenvalue problems
Behnam Hashemi, Yuji Nakatsukasa
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular general…