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- Koskela, Antti, et al.
(författare)
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On a generalization of neumann series of bessel functions using Hessenberg matrices and matrix exponentials
- 2019
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Ingår i: European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017. - Cham : Springer. - 9783319964140 ; , s. 205-214
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Konferensbidrag (refereegranskat)abstract
- The Neumann expansion of Bessel functions (of integer order) of a function g: ℂ→ ℂ corresponds to representing g as a linear combination of basis functions φ0, φ1, …, i.e., g(s)=∑ℓ=0 ∞wℓφℓ(s), where φi(s) = Ji(s), i = 0, …, are the Bessel functions. In this work, we study an expansion for a more general class of basis functions. More precisely, we assume that the basis functions satisfy an infinite dimensional linear ordinary differential equation associated with a Hessenberg matrix, motivated by the fact that these basis functions occur in certain iterative methods. A procedure to compute the basis functions as well as the coefficients is proposed. Theoretical properties of the expansion are studied. We illustrate that non-standard basis functions can give faster convergence than the Bessel functions.
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