![]() |
Reference documentation for deal.II version 8.1.0
|
#include <polynomial.h>
Public Member Functions | |
HermiteInterpolation (const unsigned int p) | |
![]() | |
Polynomial (const std::vector< double > &coefficients) | |
Polynomial (const unsigned int n) | |
Polynomial (const std::vector< Point< 1 > > &lagrange_support_points, const unsigned int evaluation_point) | |
Polynomial () | |
double | value (const doublex) const |
void | value (const doublex, std::vector< double > &values) const |
unsigned int | degree () const |
void | scale (const doublefactor) |
void | shift (const number2 offset) |
Polynomial< double > | derivative () const |
Polynomial< double > | primitive () const |
Polynomial< double > & | operator*= (const double s) |
Polynomial< double > & | operator*= (const Polynomial< double > &p) |
Polynomial< double > & | operator+= (const Polynomial< double > &p) |
Polynomial< double > & | operator-= (const Polynomial< double > &p) |
bool | operator== (const Polynomial< double > &p) const |
void | print (std::ostream &out) const |
void | serialize (Archive &ar, const unsigned int version) |
![]() | |
Subscriptor () | |
Subscriptor (const Subscriptor &) | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
void | subscribe (const char *identifier=0) const |
void | unsubscribe (const char *identifier=0) const |
unsigned int | n_subscriptions () const |
void | list_subscribers () const |
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.") | |
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1) | |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
static std::vector< Polynomial< double > > | generate_complete_basis (const unsigned int p) |
Additional Inherited Members | |
![]() | |
void | transform_into_standard_form () |
![]() | |
static void | scale (std::vector< double > &coefficients, const doublefactor) |
static void | shift (std::vector< double > &coefficients, const number2 shift) |
static void | multiply (std::vector< double > &coefficients, const doublefactor) |
![]() | |
std::vector< double > | coefficients |
bool | in_lagrange_product_form |
std::vector< double > | lagrange_support_points |
double | lagrange_weight |
Polynomials for Hermite interpolation condition.
This is the set of polynomials of degree at least three, such that the following interpolation conditions are met: the polynomials and their first derivatives vanish at the values x=0 and x=1, with the exceptions p0(0)=1, p1(1)=1, p'2(0)=1, p'3(1)=1.
For degree three, we obtain the standard four Hermitian interpolation polynomials, see for instance Wikipedia. For higher degrees, these are augmented first, by the polynomial of degree four with vanishing values and derivatives at x=0 and x=1, then by the product of this fourth order polynomial with Legendre polynomials of increasing order. The implementation is
Definition at line 632 of file polynomial.h.
Polynomials::HermiteInterpolation::HermiteInterpolation | ( | const unsigned int | p | ) |
Constructor for polynomial with index p
. See the class documentation on the definition of the sequence of polynomials.
|
static |
Return the polynomials with index 0
up to p+1
in a space of degree up to p
. Here, p
has to be at least 3.