Results 141 to 150 of about 906 (173)

n-Orthonormal Operator Polynomials

1988
If μ, is a positive Borel measure with infinite support on the unit circle T in the complex plane C, then the Gram-Schmidt process applied in L 2(μ) to the sequence of polynomials 1, z, z 2,..., yields an orthonormal sequence of polynomials in L 2(μ).
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Local Representation of the Geopotential by Weighted Orthonormal Polynomials

Journal of Guidance and Control, 1979
The finite-element model of the geopotential and its gradient as introduced by Junkins, is significantly improved by the use of orthonormal polynomials. The computational effort to obtain the modeling constants via the normal equations is greatly reduced, especially if the order of approximation is increased.
Engels, Remi C., Junkins, John L.
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Use of orthonormal polynomials in calibration problems

Computer Physics Communications, 1981
Abstract A general approach to calibration problems is proposed. It is based on the use of polynomials orthonormal over discrete point sets with arbitrary positive weights. These are numerically built by means of recurrence relations of the Forsythe-Weisfeld type.
N. Bogdanova, V. Gadjokov
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Prediction with orthonormal polynomials in overlapping windows

Il Nuovo Cimento B Series 11, 1993
We propose a polynomial-expansion procedure with overlapping windows in which strong local curvature or non-polynomial behavior in the map can be isolated and better resolved than in a global polynomial expansion. The method is tested on 1-D maps and compared to the global expansion.
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Boundedness in the mean of orthonormalized polynomials

Mathematical Notes of the Academy of Sciences of the USSR, 1973
For the polynomials {pn(t)} 0 ∞ , orthonormalized on [−1, 1] with weightp(t) = (1−t)α (1+t)β∏ v=1 , we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
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Aberration balancing, orthonormal polynomials, and wavefront analysis

Frontiers in Optics 2012/Laser Science XXVIII, 2012
Starting with the Zernike circle polynomials for wavefront analysis of rotationally symmetric systems, we discuss the corresponding polynomials for noncircular pupils such as elliptical or rectangular. We also consider such polynomials for anamorphic systems.
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Parameterization of reaction mechanisms using orthonormal polynomials

Computers & Chemistry, 1994
Abstract Recent methods for mechanism reduction convert large detailed chemical reaction mechanisms into small systems of differential or differential-algebraic equations. A possible further step is the parameterization of reaction mechanisms, i.e.
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Orthonormal Polynomials

2009
Hiroyuki Shima, Tsuneyoshi Nakayama
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On Local Asymptotics for Orthonormal Polynomials

2023
Eli Levin, D. S. Lubinsky
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Jensen polynomials for the Riemann zeta function and other sequences

Proceedings of the National Academy of Sciences of the United States of America, 2019
Larry G Rolen
exaly