taylorInterval

An interval-based linear approximation with explicit error bounds.

[ kepler | Source | Keywords | Summary | Ancestors | All Members | Descendants ]

Quick Index

OVERVIEW TEXT
AUTHOR

Class Summary

class taylorInterval

{

public:
int isValidData() const;
lineInterval center() const;
double upperBound() const;
double lowerBound() const;
static double upperboundQ (const taylorInterval& cA,const taylorInterval& cB);
static double lowerboundQ (const taylorInterval& cA,const taylorInterval& cB);
double upperPartial(int) const;
double lowerPartial(int) const;
taylorInterval(int,const lineInterval&, const domain&, const double [6][6]);
protected:
}; // taylorInterval

Back to the top of taylorInterval


OVERVIEW TEXT

A taylorInterval is a souped-up version of lineInterval, which in turn is an enhancement of interval. A taylorInterval is an interval version of a linear approximation to a function with explicit bounds on the error term.

Because error terms on the second derivatives are included, explicit lower and upper bounds, as well as bounds on the derivatives can be determined.

A taylorInterval may contain invalid data, meaning that error bounds were impossible to obtain on the given domain. Calling most of the functions will result in an error if the data is invalid. To avoid the error messages, check the data with the member function isValidData().

Back to the top of taylorInterval


AUTHOR

Thomas C. Hales

Back to the top of taylorInterval


int isValidData() const;

Return a nonzero value if the data is valid, 0 otherwise.

int isValidData() const;

Back to the top of taylorInterval


lineInterval center() const;

Taylor interval is a linear approximation at the center of a cell with explicit error bounds. center() is the lineInterval giving the linear approximation at the center of the cell.

lineInterval center() const;

Back to the top of taylorInterval


double upperBound() const;

A rigorous upper bound on the value over the entire cell.

double upperBound() const;

Back to the top of taylorInterval


double lowerBound() const;

A rigorous lower bound on the value over an entire cell.

double lowerBound() const;

Back to the top of taylorInterval


double upperboundQ (const taylorInterval& cA,const taylorInterval& cB);

A rigorous upper bound on the combined value of two simplices sharing edges 2,3,4. In general this bound will be better than combining the bounds for the two separate simplices.

static double upperboundQ
    (const taylorInterval& cA,const taylorInterval& cB);

Back to the top of taylorInterval


double lowerboundQ (const taylorInterval& cA,const taylorInterval& cB);

A rigorous lower bound on the combined value of two simplices sharing edges 2,3,4. In general this bound will be better than combining the bounds for the two separate simplices.

static double lowerboundQ
    (const taylorInterval& cA,const taylorInterval& cB);

Back to the top of taylorInterval


double upperPartial(int) const;

A rigorous upper bound on the ith partial derivative over the entire cell.

double upperPartial(int) const;

Back to the top of taylorInterval


double lowerPartial(int) const;

A rigorous lower bound on the ith partial deriviative over the entire cell.

double lowerPartial(int) const;

Back to the top of taylorInterval


taylorInterval(int,const lineInterval&, const domain&, const double [6][6]);

A constructor, taking the lineInterval at the center, a bound on the half-widths of the cell (domain&), an an array [][] of doubles giving bounds on the second derivatives the first argument is nonzero or zero depending on whether the input is valid or not.

taylorInterval(int,const lineInterval&, const domain&,
        const double [6][6]);

Back to the top of taylorInterval


All Members

public:
int isValidData() const;
lineInterval center() const;
double upperBound() const;
double lowerBound() const;
static double upperboundQ (const taylorInterval& cA,const taylorInterval& cB);
static double lowerboundQ (const taylorInterval& cA,const taylorInterval& cB);
double upperPartial(int) const;
double lowerPartial(int) const;
protected:

Back to the top of taylorInterval


Ancestors

Class does not inherit from any other class.

Back to the top of taylorInterval


Descendants

Class is not inherited by any others.

Back to the top of taylorInterval


Generated from source by the Cocoon utilities on Mon Dec 22 19:37:25 1997 .

Report problems to jkotula@unimax.com