title: The trigonometric polynomial like Bernstein polynomial.
abstract: A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given.
authors.affiliation: School of Mathematics and Statistics, Central South University, Changsha 410083, China.
authors.forename: Xuli
authors.identifier: 0000-0001-7708-6971
authors.initials: X
authors.lastname: Han
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods; D008962:Models, Theoretical; D015203:Reproducibility of Results