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math.NA2025
Spectral Approximation to Fractional Integral Operators
Xiaolin Liu, Kuan Xu
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method u…
math.NA2025
A continuous approach to computing the pseudospectra of linear operators
Kuan Deng, Xiaolin Liu, Kuan Xu
We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Ins…
math.NA2024
Spectral approximation of convolution operators of Fredholm type
Xiaolin Liu, Kuan Deng, Kuan Xu
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage o…