What is Jackson's constant?

2026/07/25 by Rikhav Shah, John Urschel, Nicholas West
#math.NA #cs.NA

paper · pdf

Abstract

We prove a refinement of Jackson's theorem on the approximation of Lipschitz functions by trigonometric polynomials. Our result precisely characterizes the leading error term associated with Jackson's construction. We do the same for a related construction commonly used in the kernel polynomial method for spectral density estimation, which is slightly better than Jackson's construction in this respect.

Citations

• Sharper Bounds for Chebyshev Moment Matching, with Applications
• Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method
• The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
• Approximating spectral densities of large matrices

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• Functions measuring smoothness and the constants in Jackson--Stechkin theorem
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• Bohr--Favard Inequality for differences and constants in Jackson--Stechkin Theorem