## Numerical Computation of the Mapping Degree using Computational Homology

- Ken Nakakura, Sunao Murashige
- 12th GAMM - IMACS International Symposium on…
- 2006

@article{Murashige2006APM, title={A Practical Method of Numerical Calculation of the Mapping Degree}, author={Sunao Murashige}, journal={IEICE Transactions}, year={2006}, volume={89-A}, pages={1813-1819} }

- Published 2006 in IEICE Transactions
DOI:10.1093/ietfec/e89-a.6.1813

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… CONTINUE READING