# taylorInterval

An interval-based linear approximation with explicit error bounds.

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

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

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### 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().

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### AUTHOR

Thomas C. Hales

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### int isValidData() const;

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

```int isValidData() const;
```

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### 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;
```

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### double upperBound() const;

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

```double upperBound() const;
```

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### double lowerBound() const;

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

```double lowerBound() const;
```

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### 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);
```

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### 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);
```

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### double upperPartial(int) const;

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

```double upperPartial(int) const;
```

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### double lowerPartial(int) const;

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

```double lowerPartial(int) const;
```

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### 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]);
```

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## 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:

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## Ancestors

Class does not inherit from any other class.

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## Descendants

Class is not inherited by any others.

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

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