caa a22 4500 467939101 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7610-7 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7610-7 Construction of orthonormal multi-wavelets with additional vanishing moments [Elektronische Daten] [Charles Chui, Jian-ao Lian] An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let φ=[φ1,. . .,φr]⊤ be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and ψ=[ψ1,. . .,ψr]⊤ an o.n. multi-wavelet corresponding to φ, with two-scale symbols P and Q, respectively. Then a new (r+1)-dimensional o.n. scaling function vector φ♯:=[φ⊤,φr+1]⊤ and some corresponding o.n. multi-wavelet ψ♯ are constructed in such a way that φ♯ has p.p.o.=n>m and their two-scale symbols P♯ and Q♯ are lower and upper triangular block matrices, respectively, without increasing the size of the supports. For instance, for r=1, if we consider the mth order Daubechies o.n. scaling function φ m D , then φ♯:=[φ m D ,φ2]⊤ is a scaling function vector with p.p.o. >m. As another example, for r=2, if we use the symmetric o.n. scaling function vector φ in our earlier work, then we obtain a new pair of scaling function vector φ♯=[φ⊤,φ3]⊤ and multi-wavelet ψ♯ that not only increase the order of vanishing moments but also preserve symmetry. Springer, 2006 scaling function vectors nationallicence multi-wavelets nationallicence two-scale symbols nationallicence two-scale equations nationallicence orthonormality nationallicence compactly supported functions nationallicence Chui Charles Department of Mathematics & Computer Science, University of Missouri-St. Louis, St. Louis, MO 63121, USA, and Department of Statistics, Stanford University, 94305, Stanford, CA, U.S.A. aut Lian Jian-ao Department of Mathematics, Prairie View A&M University, 77446, Prairie View, TX, U.S.A. aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 239-262 1019-7168 24:1-4<239 2006 24 10444 https://doi.org/10.1007/s10444-004-7610-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7610-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chui Charles Department of Mathematics & Computer Science, University of Missouri-St. Louis, St. Louis, MO 63121, USA, and Department of Statistics, Stanford University, 94305, Stanford, CA, U.S.A aut NATIONALLICENCE 700 1- Lian Jian-ao Department of Mathematics, Prairie View A&M University, 77446, Prairie View, TX, U.S.A aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 239-262 1019-7168 24:1-4<239 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer