6 papers
Fast spectral methods for Volterra integral equations
Xi Chen, Kuan Xu
We develop novel methods for the fast construction of spectral approximations to smooth linear and weakly singular Volterra integral operators and for the fast evaluation of smooth…
Recycling singular and projection subspaces for pseudospectra computation
Kuan Deng, Kuan Xu
Computing matrix pseudospectra over a prescribed region requires evaluating the smallest singular value of at a large number of grid points, which can be prohibitively expen…
Fractional calculus via variable-transform-based spectral approximations
Xiaolin Liu, Kuan Xu
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebysh…
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…
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…
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…