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Expansion of the Orthogonal Basis in Video Compression
Vestnik komp'iuternykh i informatsionnykh tekhnologii, 2014This 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 +1 more
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Function approximation with an orthogonal basis net
1990 IJCNN International Joint Conference on Neural Networks, 1990An 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 +4 more
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An orthogonal basis approach to formation shape control
Automatica, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tairan Liu, Marcio de Queiroz
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ON AN ORTHOGONAL TRIGONOMETRIC BASIS
Mathematics of the USSR-Sbornik, 1992See the review in Zbl 0758.42003.
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Orthogonal Basis for Wavelet Flows
Journal of Mathematical Sciences, 2016The 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.
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A Measure for the Non-Orthogonality of a Lattice Basis
Combinatorics, Probability and Computing, 1999Let 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
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Change of Basis for Products of Orthogonal Polynomials
SIAM Journal on Algebraic Discrete Methods, 1987Let 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
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Lebesgue Constraints for an Orthogonal Polynomial Schauder Basis
Journal of Computational Analysis and Applications, 2000The 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
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Orbital‐orthogonality constraints and basis‐set optimization
Journal of Computational Chemistry, 2006AbstractA new procedure is presented for introducing arbitrary orbital‐orthogonality constraints in the variational optimization of otherwise nonorthogonal multiconfiguration electronic wave functions. It is based on suitable analytical changes to the expressions for the first and second derivatives of the electronic energy with respect to the ...
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AN ORTHOGONAL BASIS OF A LOCAL FIELD
Mathematics of the USSR-Izvestiya, 1973An effective construction is given of an orthogonal basis for a local field, starting from the Safarevic basis.Bibliography: 4 titles.
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