3 papers
math.NA2021
The mysteries of the best approximation and Chebyshev expansion for the function with logarithmic regularities
Xiaolong Zhang
The best polynomial approximation and Chebyshev approximation are both important in numerical analysis. In tradition, the best approximation is regarded as more better than the Che…
math.NA2021
Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases
Xiaolong Zhang, John P. Boyd
When solving differential equations by a spectral method, it is often convenient to shift from Chebyshev polynomials with coefficients to modified basis function…
math.NA2016
A new analytic method with a convergence-control parameter for solving nonlinear problems
Xiaolong Zhang, Songxin Liang
In this paper, a new analytic method with a convergence-control parameter is first proposed. The parameter is used to adjust and control the convergence region and rate of…