arXiv
Open Access
2013
Efficient Calculation of Determinants of Symbolic Matrices with Many Variables
Tanya Khovanova
Ziv Scully
Abstrak
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant algorithms for numerical matrices are often not the fastest for symbolic matrices with many variables. We compare the performance of two algorithms, fraction-free Gaussian elimination and minor expansion, on symbolic matrices with many variables. We show that, under a simplified theoretical model, minor expansion is faster in most situations. We then propose optimizations for minor expansion and demonstrate their effectiveness with empirical data.
Topik & Kata Kunci
Penulis (2)
T
Tanya Khovanova
Z
Ziv Scully
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2013
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- en
- Sumber Database
- arXiv
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- Open Access ✓