newton.h File Reference

Implementation of Newton correction computation. More...

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Functions
MPS_BEGIN_DECLS void	mps_fnewton (mps_context *st, mps_polynomial *p, mps_approximation *root, cplx_t corr)
	Compute the Newton correction, i.e. and the value given by:
void	mps_dnewton (mps_context *st, mps_polynomial *p, mps_approximation *root, cdpe_t corr)
	Compute the Newton correction, i.e. and the value given by:
void	mps_mnewton (mps_context *st, mps_polynomial *p, mps_approximation *root, mpc_t corr, long int wp)
	Compute the Newton correction, i.e. and the value given by:

Detailed Description

Implementation of Newton correction computation.

Function Documentation

mps_dnewton()

void mps_dnewton	(	mps_context *	s,
		mps_polynomial *	poly,
		mps_approximation *	root,
		cdpe_t	corr )

Compute the Newton correction, i.e. and the value given by:

and set the parameter cont to true if the newton correction is greater than and to false otherwise.

This routine is the DPE version of mps_fnewton().

Parameters

s	The mps_context struct pointer.
poly	The polynomial to evaluate, casted to a mps_polynomial.
root	The approximation where the newton fraction should be evaluated.
corr	The complex value of the newton correction.

See also

mps_fnewton()

mps_fnewton()

MPS_BEGIN_DECLS void mps_fnewton	(	mps_context *	s,
		mps_polynomial *	poly,
		mps_approximation *	root,
		cplx_t	corr )

Compute the Newton correction, i.e. and the value given by:

and set the parameter cont to true if the newton correction is greater than and to false otherwise.

Parameters

s	The mps_context struct pointer.
poly	The polynomial to evaluate, casted to a mps_polynomial.
root	The approximation where the newton fraction should be evaluated.
corr	The complex value of the newton correction.

mps_mnewton()

void mps_mnewton	(	mps_context *	s,
		mps_polynomial *	poly,
		mps_approximation *	root,
		mpc_t	corr,
		long int	wp )

Compute the Newton correction, i.e. and the value given by:

and set the parameter cont to true if the newton correction is greater than and to false otherwise.

This routine is the multiprecision version of mps_fnewton(). It differs from these routines, indeed, because it uses a more sophisticated tecnique to perform the computation:

• If the polynomial are dense the computation is performed with the Horner's rule
• If the polynomial is sparse then the computation is performed with the parallel Horner algorithm.

Parameters

s	The mps_context struct pointer.
poly	The polynomial to evaluate, casted to a mps_polynomial.
root	The approximation where the newton fraction should be evaluated.
corr	The complex value of the newton correction.
wp	Select the working precision to use in the computation.

See also

mps_fnewton()

mps_dnewton()