A Practical Method of Numerical Calculation of the Mapping Degree
Summary :
This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.6 pp.1813-1819
- Publication Date
- 2006/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e89-a.6.1813
- Type of Manuscript
- PAPER
- Category
- Numerical Analysis and Optimization
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Sunao MURASHIGE, "A Practical Method of Numerical Calculation of the Mapping Degree" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 6, pp. 1813-1819, June 2006, doi: 10.1093/ietfec/e89-a.6.1813.
Abstract: This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.6.1813/_p
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@ARTICLE{e89-a_6_1813,
author={Sunao MURASHIGE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Practical Method of Numerical Calculation of the Mapping Degree},
year={2006},
volume={E89-A},
number={6},
pages={1813-1819},
abstract={This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.},
keywords={},
doi={10.1093/ietfec/e89-a.6.1813},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - A Practical Method of Numerical Calculation of the Mapping Degree
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1813
EP - 1819
AU - Sunao MURASHIGE
PY - 2006
DO - 10.1093/ietfec/e89-a.6.1813
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2006
AB - This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.
ER -
English
