Title: On Multivariate Polynomial L1 — Approximation to Zero and Related Coefficient Inequalities
Abstract: It is well known (cf. TIMAN /12/, pp.66) that among all monic univariate polynomials of degree n the n-th normalized orthogonal polynomial with respect to the weight function wp, given by wp(x)=(1-x2)1/p -1/2,is the best approximation to zero on I = [-1,1] in the LP-sense, $$p \in \{ 1,2,\infty \}$$ . It is also true that among all polynomials of degree ≤ n with second leading coefficient equal to 1 the corresponding monic orthogonal polynomial of degree n - 1 deviates least form zero on I in the LP-sense.
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot