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SIAMNUM
2010
87views more  SIAMNUM 2010»
13 years 2 months ago
A Note on the Computation of All Zeros of Simple Quaternionic Polynomials
Polynomials with quaternionic coefficients located on only one side of the powers (we call them simple polynomials) may have two different types of zeros: isolated and spherical ze...
Drahoslava Janovská, Gerhard Opfer
ICMS
2010
13 years 5 months ago
Efficient Evaluation of Large Polynomials
Abstract. Minimizing the evaluation cost of a polynomial expression is a fundamental problem in computer science. We propose tools that, for a polynomial P given as the sum of its ...
Charles E. Leiserson, Liyun Li, Marc Moreno Maza, ...
TCS
2008
13 years 7 months ago
Real algebraic numbers and polynomial systems of small degree
We present exact and complete algorithms based on precomputed Sturm-Habicht sequences, discriminants and invariants, that classify, isolate with rational points and compare the re...
Ioannis Z. Emiris, Elias P. Tsigaridas
MOC
2011
12 years 10 months ago
Calculating cyclotomic polynomials
Abstract. We present three algorithms to calculate Φn(z), the nth cyclotomic polynomial. The first algorithm calculates Φn(z) by a series of polynomial divisions, which we perfo...
Andrew Arnold, Michael B. Monagan
SIAMSC
2008
99views more  SIAMSC 2008»
13 years 7 months ago
Monte Carlo Greeks for Financial Products via Approximative Transition Densities
In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities ("Greeks"). These estimators are ba...
Jörg Kampen, Anastasia Kolodko, John Schoenma...