Basc: constrained approximation by semidefinite programming

被引：7

作者：

Foucart, Simon ^{[1
]}

Powers, Vladlena ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Columbia Univ, Ind Engn & Operat Res Dept, 500 West 120th St, New York, NY 10027 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2017年 / 37卷 / 02期

基金：

美国国家科学基金会;

关键词：

constrained approximation; simultaneous approximation; semidefinite programming; Riesz-Fejer theorem; non-negative polynomials;

D O I：

10.1093/imanum/drw014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article details the theoretical grounds for a semidefinite-programming- based method that computes best approximants by splines under some general constraints and relative to several function norms, notably the max-norm. The method has been implemented as a matlab package called Basc (Best Approximations by Splines under Constraints), which relies on the two external packages Chebfun and CVX.

引用

页码：1066 / 1085

页数：20

共 14 条

[1]

[Anonymous], 2013, APPROXIMATION THEORY

[2] On the best approximation of vertical bar x vertical bar by polynomic linear data. [J].

Bernstein, S .

ACTA MATHEMATICA, 1914, 37 (01) :1-57

[3]

CHALMERS BL, 1976, T AM MATH SOC, V223, P103

[4]

CVX Research Inc., 2014, SOFTW DISC CONV PROG

[5]

Dumitrescu B., 2007, Positive Trigonometric Polynomials and Signal Processing Applications

[6] CHARACTERIZATION THEOREMS FOR CONSTRAINED APPROXIMATION PROBLEMS VIA OPTIMIZATION THEORY [J].

GEHNER, KR .

JOURNAL OF APPROXIMATION THEORY, 1975, 14 (01) :51-76

[7]

Kopotun K.A., 2011, Surv. Approx. Theory, V6, P24

[8]

Kroo Andras., 2010, Surv. Approx. Theory, V5, P1

[9] APPROXIMATION WITH CONVEX CONSTRAINTS [J].

LEWIS, JT .

SIAM REVIEW, 1973, 15 (01) :193-217

[10] Discrete transforms, semidefinite programming, and sum-of-squares representations of nonnegative polynomials [J].

Roh, T ;

Vandenberghe, L .

SIAM JOURNAL ON OPTIMIZATION, 2006, 16 (04) :939-964

← 1 2 →