Richardson's iterative method for surface interpolation

被引：4
作者：
Carnicer, J. M. [1 ]
Delgado, J. [1 ]
Pena, J. M. [1 ]
机构：
[1] Univ Zaragoza, Dept Matemat Aplicada IUMA, Zaragoza, Spain
来源：
BIT NUMERICAL MATHEMATICS | 2013年 / 53卷 / 02期
关键词：
Richardson's iterations; Progressive iteration approximation; Interpolation; Tensor product surfaces; Triangular surfaces; TOTALLY POSITIVE BASES; APPROXIMATION;
D O I：
10.1007/s10543-012-0411-3
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Richardson's iterative method has been used for approximating interpolating surfaces. We propose efficient modifications for tensor product surfaces that require less computational cost and storage, as well as faster convergence. Also, we consider some aspects of the triangular case together with some counter examples.
引用
收藏
页码：385 / 396
页数：12
相关论文
共 14 条
[1]   TOTALLY POSITIVE MATRICES [J].
ANDO, T .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 90 :165-219
[2]  
[Anonymous], 1991, TOPICS MATRIX ANAL, DOI DOI 10.1017/CBO9780511840371
[3]   On the progressive iteration approximation property and alternative iterations [J].
Carnicer, J. M. ;
Delgado, J. ;
Pena, J. M. .
COMPUTER AIDED GEOMETRIC DESIGN, 2011, 28 (09) :523-526
[4]   Progressive iteration approximation and the geometric algorithm [J].
Carnicer, J. M. ;
Delgado, J. ;
Pena, J. M. .
COMPUTER-AIDED DESIGN, 2012, 44 (02) :143-145
[5]   Richardson method and totally nonnegative linear systems [J].
Carnicer, J. M. ;
Delgado, J. ;
Pena, J. M. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (11-12) :2010-2017
[6]  
Carnicer J. M., 1993, ADV COMPUT MATH, V1, P173, DOI [10.1007/BF02071384, DOI 10.1007/BF02071384]
[7]   TOTALLY POSITIVE BASES FOR SHAPE-PRESERVING CURVE DESIGN AND OPTIMALITY OF B-SPLINES [J].
CARNICER, JM ;
PENA, JM .
COMPUTER AIDED GEOMETRIC DESIGN, 1994, 11 (06) :633-654
[8]   Progressive iterative approximation for triangular Bezier surfaces [J].
Chen, Jie ;
Wang, Guo-Jin .
COMPUTER-AIDED DESIGN, 2011, 43 (08) :889-895
[9]   The diagonalisation of the multivariate Bernstein operator [J].
Cooper, S ;
Waldron, S .
JOURNAL OF APPROXIMATION THEORY, 2002, 117 (01) :103-131
[10]   Progressive iterative approximation and bases with the fastest convergence rates [J].
Delgado, J. ;
Pena, J. M. .
COMPUTER AIDED GEOMETRIC DESIGN, 2007, 24 (01) :10-18
12