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An algorithm for constructing biorthogonal multiwavelets with higher approximation orders

Yang Shouzhi
2006 ANZIAM journal (Print)  
Given a pair of biorthogonal multiscaling functions, we present an algorithm for raising their approximation orders to any desired level. Precisely, let 8.x/ and8.x/ be a pair of biorthogonal multiscaling functions of multiplicity r , with approximation orders m andm, respectively. Then for some integer s, we can construct a pair of new biorthogonal multiscaling functions 8 new .x/ = [8 T .x/; r +1 .x/; r +2 .x/; : : : ; r +s .x/] T and8 new .x/ = [8.x/ T ;˜ r +1 .x/;˜ r +2 .x/; : : : ;˜ r +s
more » ... x/; : : : ;˜ r +s .x/] T with approximation orders n (n > m) andñ (ñ >m), respectively. In addition, corresponding to 8 new .x/ and8 new .x/, a biorthogonal multiwavelet pair 9 new .x/ and9 new .x/ is constructed explicitly. Finally, an example is given. 2000 Mathematics subject classification: primary 42C15, 94A12.
doi:10.1017/s1446181100010105 fatcat:g3sswu333rcexkh3aa7lp2q6ri