Files | |
file | jenkinstraub.h |
file | laguerre.h |
file | muller.h |
file | Polynomial.h |
file | polyzero.h |
Modules | |
Polynomial evaluation functions | |
Polynomial arithmetics functions | |
Polynomial roots-solving functions | |
Classes | |
class | Polynomial< T > |
Functions | |
template<class T> | |
T | getOptimalScale (const Polynomial< T > &p) |
template<class T, class U> | |
U | scalePoly (Polynomial< T > &p, const Polynomial< U > &q) |
template<class T, class U> | |
void | modulus (const Polynomial< T > &p, Polynomial< U > &q) |
template<class T> | |
T | cauchyLowerBound (const Polynomial< T > &p, const T &upperBound=T(0)) |
template<class T> | |
T | cauchyUpperBound (const Polynomial< T > &p) |
template<class T> | |
T | zerosGeometricMean (const Polynomial< T > &p) |
template<class T> | |
T | zerosGeometricMean (const Polynomial< std::complex< T > > &p) |
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returns the Cauchy lower bound for a polynomial. approximates the Cauchy lower bound for polynomial p. This function expects the input polynomial to be of the form:
where The optional parameter upperBound indicates a starting point from where to start looking for this zero. If upperBound is omited, or null, the geometric mean of the zeros will be used as a starting point for the search.
Definition at line 233 of file polyzero.h. |
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returns the Cauchy upper bound for a polynomial Returns the Cauchy upper bound for polynomial p.
The Cauchy upper bound
Definition at line 266 of file polyzero.h. |
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returns optimal scale for polynomial. Computes an optimal scale factor for polynomial p. Thus ensuring that evaluating the polynomial will not result in overflow or underflow.
Definition at line 1253 of file Polynomial.h. |
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computes the modulus of polynomial p. Computes the modulus of polynomial p, such as for polynomial:
the resulting polynomial q will be :
Definition at line 1315 of file Polynomial.h. |
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rescales a polynomial using an optimal scale. Computes an optimal scale factor for polynomial p. Thus ensuring that evaluating the polynomial will not result in overflow or underflow, then scales the polynomial p.
Definition at line 1293 of file Polynomial.h. |
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returns the geometric mean for zeros of a polynomial. See zerosGeometricMean(const Polynomial<T>& p) for more details. Definition at line 306 of file polyzero.h. |
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returns the geometric mean for zeros of a polynomial. Returns the geometric mean for zeros of a polynomial.
According to Vieta's theorem, the geometric mean
Definition at line 293 of file polyzero.h. |