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Revisiting the inverse Abel integral for reconstructing velocity-map images. [PDF]
Sparling C, Onvlee J.
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Simultaneous Polynomial Approximation
SIAM Journal on Mathematical Analysis, 1993The authors prove the approximation theorem on simultaneous approximation of \(f\in C^ s[- 1,1]\) and its derivatives of order \(j\), \(0\leq j\leq s\), by polynomials of degree \(n\) and their derivatives which has filled the gap between Timan-Trigub's type theorem and the classical norm estimate of the Jackson type.
Ditzian, Z. +2 more
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Approximate polynomial decomposition
Proceedings of the 1999 international symposium on Symbolic and algebraic computation, 1999where deg g < deg f , deg h < deg f , deg∆f ≤ deg f and ∆f is “small” with respect to the 2-norm of the vector of coefficients. In practice if ‖f‖ denotes the 2-norm of f , then we compute g and h such that ‖∆f‖ is a local minimum with respect to variations in g and h.
Robert M. Corless +3 more
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Approximate Polynomial GCD by Approximate Syzygies
Mathematics in Computer Science, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximation in the Mean by Polynomials
The Annals of Mathematics, 1991Let \(\mu\) be a positive measure with compact support in the complex plane and let \(t\in[1,\infty)\). Denote by \(P^ t(\mu)\) the closure in \(L^ t(\mu)\) of the polynomials in one complex variable. The paper deals with the description of \(P^ t(\mu)\). The main results are the following: There exists a Borel partition \(\{\Delta_ i\}^ \infty_{i=0}\)
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Approximation Numbers for Polynomials
2019Approximation numbers of linear operators are a very useful tool in order to understand the structure and the numerical behaviour of the operators. In this paper, this concept is extended to polynomials on Banach spaces and the approximation numbers of diagonal polynomials are estimated.
Junek, Heinz +2 more
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Rigorous Polynomial Approximation
2018 52nd Asilomar Conference on Signals, Systems, and Computers, 2018Polynomial approximation is a key to implementation of transcendental functions $f: \mathrm{R}\rightarrow \mathrm{R}$, such as $\exp, \log, \sin$. All existing approaches to polynomial approximation are based on a posteriori control of the error made during the approximation process with floating-point numbers F.We perform polynomial interpolation with
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