Sampling of homogeneous polynomials and approximating multivariate functions

被引：0

作者：

Datta, Somantika ^{[1
]}

Howard, Stephen ^{[2
]}

Cochran, Douglas ^{[3
]}

机构：

[1] Univ Idaho, Dept Math, Moscow, ID 83844 USA

[2] Def Sci & Technol Org, Edinburgh, SA 5111, Australia

[3] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

来源：

ADVANCES IN PURE AND APPLIED MATHEMATICS | 2012年 / 3卷 / 04期

关键词：

Frames; homogeneous polynomials; sampling; symmetric tensors;

D O I：

10.1515/apam-2012-0028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Conditions for reconstruction of multivariate homogeneous polynomials from sets of sample values are introduced. In addition, it is shown that one can explicitly obtain the polynomial coefficients from the sample data by considering frames for spaces of symmetric tensors. Further, it is discussed how the reconstruction of homogeneous polynomials can be used to approximate certain smooth functions.

引用

页码：421 / 441

页数：21

共 13 条

[1]

[Anonymous], 1991, GRADUATE TEXTS MATH

[2]

Benko D, 2009, T AM MATH SOC, V361, P1645

[3]

Calderbank R., 2009, COMMUNICATION

[4]

Christensen O., 2003, INTRO FRAMES RIESZ B

[5] Geometry of the Welch bounds [J].

Datta, S. ;

Howard, S. ;

Cochran, D. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (10) :2455-2470

[6]

Daubechies I., 1992, CBMS NSF REGIONAL C, V61

[7] THE Z4-LINEARITY OF KERDOCK, PREPARATA, GOETHALS, AND RELATED CODES [J].

HAMMONS, AR ;

KUMAR, PV ;

CALDERBANK, AR ;

SLOANE, NJA ;

SOLE, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (02) :301-319

[8] CLASS OF LOW-RATE NONLINEAR BINARY CODES [J].

KERDOCK, AM .

INFORMATION AND CONTROL, 1972, 20 (02) :182-&

[9]

Klappenecker A, 2005, 2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), VOLS 1 AND 2, P1740

[10] Signed frames and Hadamard products of Gram matrices [J].

Peng, I ;

Waldron, S .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 347 (1-3) :131-157

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