Results 161 to 170 of about 44,437 (210)
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Orthonormal polynomials for hexagonal pupils
Optics Letters, 2006The problem of determining the orthonormal polynomials for hexagonal pupils by the Gram-Schmidt orthogonalization of Zernike circle polynomials is revisited, and closed-form expressions for the hexagonal polynomials are given. We show how the orthonormal coefficients are related to the corresponding Zernike coefficients for a hexagonal pupil and ...
Virendra N, Mahajan, Guang-ming, Dai
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Weighted fit by orthonormal polynomials
Computer Physics Communications, 1981Abstract The fitting technique by orthonormal polynomials and Forsythe's recurrence relationship, generalized in order to take into account experimental errors, are discussed. Comparison is made between orthonormal and standard fits to point out the improvements on the latter, mainly from a computational point of view.
ROSATO, ELIO +4 more
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On orthonormal harmonic polynomials
The Journal of Analysis, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heinz Leutwiler, Eleutherius Symeonidis
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Convolutions of Orthonormal Polynomials
SIAM Journal on Mathematical Analysis, 1976zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Al-Salam, W. A., Chihara, T. S.
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On the Difference of Orthonormal Polynomials
Quaestiones Mathematicae, 2003We establish an estimate on the difference of orthonormal polynomials for a general class of exponential weights. Mathematics Subject Classification (2000): 41A05, 05E35, 41A65 Key words: Orthonormal polynomials, exponential weights Quaestiones Mathematicae 26(2003), 347 ...
Kubayi D.G., Mashele H.P.
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Orthonormal polynomials in wavefront analysis: error analysis
Applied Optics, 2006Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, rectangular, and square pupils, due to their lack of orthogonality over
Guang-Ming, Dai, Virendra N, Mahajan
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Orthonormal Polynomials in Wavefront Analysis: Analytical Solution
Frontiers in Optics, 2006Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. In recent papers, we derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror. We extend our work to
Virendra N, Mahajan, Guang-ming, Dai
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Bounds on Orthonormal Polynomials for Restricted Measures
Constructive Approximation, 2023The paper investigates upper bounds for orthonormal polynomials associated with a positive Borel measure \(\mu\) on \(\mathbb{R}\), whose restriction to \((-1,1)\) coincides with a given measure \(\nu\). The main result establishes that for \(y \in \mathbb{R}\), \[ \left|p_n(\mu, y)\right| \leq \sup _{0 \leq J \leq n} \sup _{S_J}\left|S_J(y) p_{n-J ...
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Jacobi Operators and Orthonormal Matrix-Valued Polynomials. II
Ukrainian Mathematical Journal, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hatamleh, R., Zolotarev, V. A.
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