Lanczos approximation

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• ID : Q6483801

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1. The Lanczos approximation is a particularly effective method for computing values of the Gamma function to high precision.
2. To facilitate an elegant C++ implementation of the Lanczos approximation, I have written a partial C++ wrapper for the floating point functions of GMP.
3. The Lanczos approximation has fewer of these problems, provided that the coefficients are computed accurately enough.
4. The Lanczos Approximation as implemented in the Boost C++ Libraries.
5. We report that for fixed real parts of the free parameter that using complex coefficients both increases the computational cost of the Lanczos approximation while drecreasing the accuracy...
6. In mathematics, the Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964.
7. For a well-chosen constant g and a small number of terms in the series, the Lanczos approximation is accurate to within floating-point precision.
8. In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964.
9. Among others, the Padé-via-Lanczos approximation provides an efficient solution.
10. The Lanczos approximation is used to calculate Gamma function numerically.
11. The Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964.
12. Using Lanczos Approximation.
13. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation.
14. 𝑣 ℓ + 1 for the Lanczos approximation, so that the vectors 𝑟 ℓ ≡ 𝑟 ℓ ( 0 ) and 𝑟 ℓ ( 𝑡 ) are aligned; however their magnitudes are different.
15. It is also worth pointing out that the Lanczos approximation for this preconditioned matrix function reduces much more rapidly than for the case where preconditioning (dotted line) is not used.
16. The Lanczos approximation in this example again lies almost entirely on the curve that represents the optimal approximation obtainable from the Krylov subspace.