Hokkaido Mathematical Journal

Numerical treatment of analytic continuation with Multiple-precision arithmetic

Hiroshi FUJIWARA, Hitoshi IMAI, Toshiki TAKEUCHI, and Yuusuke ISO

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Abstract

The aim of this paper is to show numerical treatment of analytic continuation by high-accurate discretization with multiple-precision arithmetic. We deal with the Cauchy problem of the Laplace equation and an integral equation of the first kind with an analytic kernel. We propose high-accurate discretization based on the spectral method, and show some numerical examples with our proposed multiple-precision arithmetic.

Article information

Source
Hokkaido Math. J., Volume 36, Number 4 (2007), 837-847.

Dates
First available in Project Euclid: 3 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1272848036

Digital Object Identifier
doi:10.14492/hokmj/1272848036

Mathematical Reviews number (MathSciNet)
MR2378294

Zentralblatt MATH identifier
1142.65083

Subjects
Primary: 65J22: Inverse problems
Secondary: 47N40: Applications in numerical analysis [See also 65Jxx] 65J20: Improperly posed problems; regularization

Keywords
analytic continuation ill-posed problem numerical instability spectral discretization multiple-precision arithmetic

Citation

FUJIWARA, Hiroshi; IMAI, Hitoshi; TAKEUCHI, Toshiki; ISO, Yuusuke. Numerical treatment of analytic continuation with Multiple-precision arithmetic. Hokkaido Math. J. 36 (2007), no. 4, 837--847. doi:10.14492/hokmj/1272848036. https://projecteuclid.org/euclid.hokmj/1272848036


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