Construction of dual bases
نویسنده
چکیده
Let Bn := {b0, b1, . . . , bn} (n = 0, 1, . . . , N ; N ∈ N) be the sets of linearly independent functions. We give a simple method of construction the dual functions Dn := { d (n) 0 , d (n) 1 , . . . , d (n) n } (0 ≤ n ≤ N) satisfying the following conditions: spanDn = spanBn and 〈 bi, d (n) j 〉 = δij (0 ≤ i, j ≤ n ≤ N), where δii = 1, δij = 0 for i 6= j, and 〈·, ·〉 is a given inner product. The proposed algorithm allows us to construct all the sets of the dual functions D0, D1, . . . , DN in the time O(N3), where N is a natural number. Four illustrative examples presenting the possible applications of obtained results are given.
منابع مشابه
A characterization of L-dual frames and L-dual Riesz bases
This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.
متن کاملNew characterizations of fusion bases and Riesz fusion bases in Hilbert spaces
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...
متن کاملOperator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملConstruction of self-dual normal bases and their complexity
Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer search, to identify the lowest complexity of selfdual normal bases for extensions of low degree. Comparisons to similar searches amongst normal bases show t...
متن کاملA new property of dual bases and its application
In this paper, we give an efficient algorithm of degree reduction of Bézier curves with box constraints. The idea is to combine the previous iterative approach, that has been presented recently in (P. Gospodarczyk, Comput. Aided Des. 62 (2015), 143–151), with a fast method of construction of dual bases from (P. Woźny, J. Comput. Appl. Math. 260 (2014), 301–311) and a new efficient method of mod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 245 شماره
صفحات -
تاریخ انتشار 2013