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奇异两尺度相似变换的逼近阶

Approximation Order of Singular Two-scale Similarity Transforms
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摘要 对于单小波,给出了0是变换矩阵的重根时,两尺度相似变换(TST)的逼近阶.对于多小波系统,定义了新的矩阵两尺度相似变换(TST),得到了当0是变换矩阵M(0)的二重非退化特征值时(TST)逼近阶以及逼近向量的形式. For scale-wavelet in this paper, the order of singular two-scale similarity transforms has been obtained when 0 is the multiple root of transformation matrix. For multi-wavelet system, the new definition of singular two-scale similarity transforms （TST） is given at first. Second, the approximate order and the form of approximate veetorc can be obtained when 0 is the double non-degenerate eigenvalue of the M（0） .
作者 雷崇民 张光晨 黄永东
机构地区 北方民族大学信息与计算科学学院
出处 《宁夏大学学报（自然科学版）》 CAS 北大核心 2011年第4期305-310,共6页 Journal of Ningxia University(Natural Science Edition)
基金 国家自然科学基金资助项目(10961001) 教育部科学技术研究重点项目(209152)
关键词 逼近阶 逼近向量 加细面具 多尺度函数 多小波函数 approximation order approximation vector refinable mask multiscaling function multi wavelets function.
分类号 O174.2 [理学—基础数学]
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参考文献15

  • 1GOODMAN T N T, LEE S L, TANG W S. Wavelets in wandering subspaces [J]. Tran Amer Math Soc, 1993,338 (2) : 639-654.
  • 2GOODMAN T N T,LEE S L. Wavelets of multiplicity r[J]. Trans Amer Math Soc, 1994,342 (1) : 307-324.
  • 3GERONIMO JS, HARDIN DP, MASSOPUST P R. Frac tal functions and wavelet expansions based on several scal- ing functions[J]. J Approx Th, 1994,78(3) : 373-401.
  • 4COHEN A, DAUBECHIES I, PLONKA G. Regularity of refinable function vectors[J]. J Fourier Anal Appl, 1997,3(3) :295-324.
  • 5CHUI C K,LIAN J A. A study of orthonormal multi wavelets[J]. Appl Numer Math, 1996, 20 (3): 237-298.
  • 6PLONKA G. Approximation order provided by refinable function vectors [J]. Constr Aprrox, 1997 , 13 ( 2 ) : 221-244.
  • 7SHEN Z. Refinable function vectors[J]. SIAM J Math Anal,1998,29(1) :235-250.
  • 8PLONKA G,STRELA V. Construction of multiscal- ing functions with approximation and symmetry[J]. SIAM J Math Anal,1998,29(2) :481-510.
  • 9HEIL C,STRANG G,STRELA V. Approximation by translates of refinable functions[J]. Numer Math, 1996,73(1):75-94.
  • 10STRELA V. Multiwavelets: theory and applications[D]. Combridge: MIT, 1996.

二级参考文献33

  • 1YANG Shouzhi & PENG Lizhong Department of Mathematics, Shantou University, Shantou 515063, China,LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China.Raising approximation order of refinable vector by increasing multiplicity[J].Science China Mathematics,2006,49(1):86-97. 被引量：10
  • 2GOODMAN T N T, LEE S L, TANG W S. Wavelet in wandering subspace[J]. Trans Amer Math Soc, 1993 (338) : 639-654.
  • 3GOODMAN T N T, LEE S L. Wavelet of multiplitity [J]. Trans Amer Math Soc, 1994(342):307-324.
  • 4GERONIMO J, HARDIN D, MASSOPUST P R. Fractal functions and wavelet expansions based on several scaling functions[J]. J Approx Th, 1994(78) :373-401.
  • 5COHEN A, DAUBECHIES I, PLONKA G. Regularity of refinable function vectors [J]. J Fourier Anal Appl, 1997(3) :295-324.
  • 6CHUI C K, LIAN J. A study of orthonormal mutiwavelets[J]. J Appl Numer Math, 1996(20) :237-298.
  • 7PLONKA G. Approximation order provided by refinable function vectors[J]. Constr Approx, 1997 (13) : 221-244.
  • 8SHEN Z. Refinable function vectors[J]. SIAMJ Math Anal,1998(29) :235-250.
  • 9PLONKA G, STRELA V. Construction of multiscaling functions with approximation and symmetry[J]. SIAMJ Math Anal,1998(29) :481-510.
  • 10HEIL C, STRANG G, STRELA V. Approximation by translates of refinable functions[J]. Numer Math, 1996(73) :75-94.

共引文献10

宁夏大学学报（自然科学版）
2011年 第4期

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