Research Interests
- Approximation theory
- Spectral methods
- Fast algorithms
- Orthogonal polynomials
Publications
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Understanding the ultraspherical spectral method
Cheng, L. and Xu, K. Submitted (2024) |
arxiv |
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Spectral approximation of convolution operators of Fredholm type Liu, X., Deng, K., and Xu, K. Submitted (2024) |
arxiv |
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A continuous approach for computing the pseudospectra of operators Deng, K., Liu, X., and Xu, K. Submitted (2024) |
arxiv |
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Solving nonlinear ODEs with the ultraspherical spectral method
Qin, O. and Xu, K. IMA J. Numer. Anal. (2024), drad099 |
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Solving time-dependent PDEs with the ultraspherical spectral method Cheng, L. and Xu, K. J. Sci. Comput. (2023), 96:70. |
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On the backward error incurred by the compact rational Krylov linearization Chen, H. and Xu, K. J. Sci. Comput. 89 (2021), pp. 1-22. |
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Volterra-type Convolution of classical polynomials Loureiro, A. F. and Xu, K. Math. Comp. 88 (2019), pp. 2351-2381. |
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Spectral approximation of convolution operator Xu, K. and Loureiro, A. F. SIAM J. Sci. Comput. 40 (2018), no. 4, pp. A2336-A2355. |
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A fast algorithm for the convolution of functions with compact support using Fourier extensions Xu, K., Austin, A. P., and K. Wei SIAM J. Sci. Comput. 39 (2017), no. 6, pp. A3089-A3106. |
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On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points Austin, A. P. and Xu, K. IMA J. Numer. Anal. 37 (2017), pp. 1355-1374. |
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The Chebyshev points of the first kind Xu, K. Appl. Numer. Math. 102 (2016), pp. 17-30. |
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Explicit construction of rectangular differentiation matrices Xu, K. and Hale, N. IMA J. Numer. Anal. 36 (2016), pp. 618-632. |
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Extension of the continuum time-dependent Hartree-Fock method to proton states Pardi, C. I., Stevenson, P. D., and Xu, K. Phys. Rev. E 89 (2014), 033312. |
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A bootstrap method for sum-of-pole approximations Xu, K. and Jiang, S. J. Sci. Comput. 55 (2013), pp. 16-39. |
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Analytical and computational methods for two-phase flow with soluble surfactant Xu, K., Booty, M., and Siegel, M. SIAM J. Appl. Math. 73 (2013), pp. 523-548. |