Approximation on \([0,\infty)\) by reciprocals of polynomials with nonnegative coefficients
This paper considers the problem of best uniform approximation on closed subsets of \([0,\infty)\) of positive continuous functions (decaying to zero at \(\infty)\) by reciprocals of polynomials of degree \(\leq n\) with all coefficients nonnegative. Existence, characterization, (strong) uniqueness, and discretization results are given, along with several examples. It is also shown that if \(n\geq 1\), then approximation on \([0,\infty)\) is equivalent to approximation on [0,b] for some real b; b can be determined constructively. For the corresponding results in the case where only the coefficient of \(x^ n\) is required to be nonnegative, see the authors, Approximation on subsets of \([0,\infty)\) by reciprocals of polynomials, Approximation Theory IV, Academic Press, 553- 559 (1983).
scientific article; zbMATH DE number 3844323