Results 241 to 250 of about 645,441 (285)

An orthogonal basis for the hyperbolic hybrid polynomial space

Science in China Series F: Information Sciences, 2007
An orthogonal basis which is defined on the base of the \(H\)-Bézier basis in the hyperbolic hybrid polynomial space, is introduced. This orthogonal basis is characterized by the similar properties as the \(H\)-Bézier basis and properties of the \(H\)-Bézier basis are similar as properties of the Bernstein basis in the polynomial space. The reason lies
Yu Huang, Guozhao Wang
exaly   +3 more sources

Closed-Form Orthogonal Ramanujan Integer Basis

IEEE Signal Processing Letters, 2017
In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram–Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis.
Soo-Chang Pei, Kuo-Wei Chang
exaly   +2 more sources

Expansion of the Orthogonal Basis in Video Compression

Vestnik komp'iuternykh i informatsionnykh tekhnologii, 2014
This article discusses the procedure of image compression using the Hadamard-Mersenne, Hadamard-Fermat matrices and derived from them orthogonal M-matrices. At the stage of image spectral decomposition it is proposed to use the original two-tier symmetric orthogonal M-matrices order, equal to the Mersenne and Fermat primes, as well as the low frequency
Nikolay A. Balonin, Michael Borisovich Sergeev   +1 more
openaire   +1 more source

Function approximation with an orthogonal basis net

1990 IJCNN International Joint Conference on Neural Networks, 1990
An orthogonal basis net (OrthoNet) is studied for function approximation. The network transfers input space to a new space in which the orthogonal basis function is easy to construct. This net has the advantages of fast and accurate learning and the ability to deal with high-dimensional systems, and it has only one minimum, so that local minima are not
S. Qian, Yee-Chun Lee, R. D. Jones, C. W. Barnes, K. Lee   +4 more
openaire   +1 more source

An orthogonal basis approach to formation shape control

Automatica, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tairan Liu, Marcio de Queiroz
openaire   +1 more source

ON AN ORTHOGONAL TRIGONOMETRIC BASIS

Mathematics of the USSR-Sbornik, 1992
See the review in Zbl 0758.42003.
openaire   +1 more source

Orthogonal Basis for Wavelet Flows

Journal of Mathematical Sciences, 2016
The author obtains a very interesting orthogonal (in the Euclidean space) basis of discrete wavelets in the case of a spline-wavelet decomposition of the comb structure. He estimates the computation time necessary to realize this decomposition by a concurrent computing system with computer communication surrounding taken into account.
openaire   +2 more sources

A Measure for the Non-Orthogonality of a Lattice Basis

Combinatorics, Probability and Computing, 1999
Let B = [b1, …, bn] (with column vectors bi) be a basis of ℝn. Then L = [sum ]biℤ is a lattice in ℝn and A = B[top ]B is the Gram matrix of B. The reciprocal lattice L* of L has basis B* = (B−1)[top ] with Gram matrix A−1. For any nonsingular matrix A = (ai,j) with inverse A−1 = (a*i,j), let τ(A) = max1[les ]i[les ]n {[sum
openaire   +1 more source

Change of Basis for Products of Orthogonal Polynomials

SIAM Journal on Algebraic Discrete Methods, 1987
Let be given the orthogonal polynomials \(\{p_ i(\lambda)\}\), \(\{q_ i(\lambda)\}\). The author demonstrates four theorems concerning the expression of \(\lambda^ ip_ j(\lambda)\), \(\lambda^ iq_ j(\lambda)\), \(p_ i(\lambda)q_ j(\lambda)\) and \(q_ i(\lambda)q_ j(\lambda)\) in terms of \(p_ i(\lambda)\). The proofs are based on a former result of the
openaire   +1 more source

Lebesgue Constraints for an Orthogonal Polynomial Schauder Basis

Journal of Computational Analysis and Applications, 2000
The paper contains a clear exposition of the ideas and methods used in the construction of a class of orthogonal polynomial Schauder bases of optimal degree for the space \(C[-1,1]\) with the Chebyshev weight of the first kind. The authors give also all details of the proof for the estimation of the Lebesgue constants of those bases.
Girgensohn, Roland, Prestin, Jürgen
openaire   +1 more source