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A Basis-Kernel Representation of Orthogonal Matrices
SIAM Journal on Matrix Analysis and Applications, 1995It is shown that any orthogonal matrix \(Q \in M_{mm}\) can be represented in the form \(Q = I - YSY^T\) \((Y \in M_{mk}\), \(S \in M_{kk}\), \(k = rk(Y) = rk(S) = rk(I - Q))\) and that the ``kernel'' \(S\) can be chosen to be triangular.
Christian Bischof, Xiaobai Sun
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Legendre-like orthogonal basis for spline space
CAD Computer Aided Design, 2013The usual B-spline basis is not orthogonal. In order to resolve the theoretical problem that there is not a well-expressed orthogonal basis in spline space to date, we construct an orthogonal basis for the n-degree spline space in which n is an arbitrary natural number.
Guozhao Wang
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Closed-Form Orthogonal Ramanujan Integer Basis
IEEE Signal Processing Letters, 2017In 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.
Kuo-Wei Chang, Soo-Chang Pei
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An orthogonal basis for the hyperbolic hybrid polynomial space
Science in China Series F: Information Sciences, 2007An 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
Guozhao Wang, Wang Guozhao
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