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math.NA2026
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…
math.NA2026
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…
math.NA2026
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…