On the cell probe complexity of polynomial evaluation
β Scribed by Peter Bro Miltersen
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 461 KB
- Volume
- 143
- Category
- Article
- ISSN
- 0304-3975
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π SIMILAR VOLUMES
The approximate evaluation with a given precision of matrix and polynomial products is performed using modular arithmetic. The resulting algorithms are numerically stable. At the same time they are as fast as or faster than the algorithms with arithmetic operations over real or complex numbers.
We investigate the complexity of (1) computing the characteristic polynomial, the minimal polynomial, and all the invariant factors of an integer matrix, and of (2) verifying them, when the coe cients are given as input. It is known that each coe cient of the characteristic polynomial of a matrix A
The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH). By the works of and , the general problem reduces deterministically in polynomial time to finding a proper factor of any squarefree and completely splitting