New type multiwavelets of the fifth degree orthogonal to quintic polynomials
For the space of Hermitian splines of the fifth degree of a kind S
W = I TcL
NLk (x), a < x < b, k=0 i=0 with a uniform grid of nodes A
: u
= a + (b - a) i / 2
, i = 0, 1,..., 2
, L > 0, and the basic functions N
k
l) (uj) = Sj • Sk, l = 0,1,2 , with the centers in integers, it is proposed to use as wavelets functions M
i,k(x), satisfying the conditions of orthogonality to all polynomials of sixth order, i.e. f M
k(x)x
dx = 0, k = 0,1,2 Vi (m = 0,1,...,5). For the wavelets centered at even integers, a and the supports equal to the supports of basic splines on the grid A
, received two-scale relations of expansion and formulas for calculating the coefficients in the thinned grid A
from the spline coefficients in a dense grid A
in the form of solution of linear algebraic equations system with band matrix. There are results of numerical experiments presented. Justified the improving of compression of numerical data in comparison with the known quintic wavelets and multiwavelets.
Keywords
эрмитовы сплайны пятой степени,
мультивейвлеты,
ортогональность многочленам,
Hermitian splines of the fifth degree,
multiwavelets,
orthogonality to polynomialsAuthors
| Shumilov Boris M. | National Research Tomsk State University | b_shumilov@math.tsu.ru |
| Kuduev Altynbek Z. | Osh State University | altun_12@rambler.ru |
Всего: 2
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