com.numericalmethod.suanshu.analysis.interpolation

Class NevilleTable

java.lang.Object

com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.UnivariateRealFunction

com.numericalmethod.suanshu.analysis.interpolation.NevilleTable

All Implemented Interfaces:

Function<Vector,java.lang.Double>, RealScalarFunction, OnlineInterpolator, java.io.Serializable

public class NevilleTable
extends UnivariateRealFunction
implements OnlineInterpolator

Neville's algorithm is a polynomial interpolation algorithm. Given n + 1 points, there is a unique polynomial of degree ≤ n which associates with them. Neville's algorithm evaluates this polynomial for a given input x.

This implementation is based on filling out the Neville table. This table can be used in two ways. First, it can be used to compute the interpolated function f(x). Second, it can be used in an incremental manner by adding a few, say one, data points each time to allow for examination of the table values.

See Also:

Wikipedia: Neville's algorithm, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor and Description
NevilleTable() Construct an empty Neville table.
NevilleTable(int n, OrderedPairs f) Construct a Neville table of size n, initialized with data {(x, y)}.
NevilleTable(OrderedPairs f) Construct a Neville table of size n, initialized with data {(x, y)}.

Method Summary

Modifier and Type	Method and Description
void	addData(OrderedPairs f) Add more points for interpolation.
double	evaluate(double x) Evaluate y = f(x).
double	get(int i, int j) Get the value of a table entry.
double[][]	getTable() Get a copy of the Neville table.
int	N() Get the number of data points.
double[]	x() Get a copy of the x's.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.UnivariateRealFunction

dimensionOfDomain, dimensionOfRange, evaluate

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NevilleTable

public NevilleTable(int n,
                    OrderedPairs f)

Construct a Neville table of size n, initialized with data {(x, y)}. The size n is only indicative. If there are more data points than n, the table size grows accordingly.

Parameters:

n - indicative size; make this big for reservation to add new data points

f - the points to be interpolated

NevilleTable

public NevilleTable(OrderedPairs f)

Construct a Neville table of size n, initialized with data {(x, y)}.

Parameters:

f - the points to be interpolated

NevilleTable

public NevilleTable()

Construct an empty Neville table.

Method Detail

addData

public void addData(OrderedPairs f)

Description copied from interface: OnlineInterpolator

Add more points for interpolation.

Specified by:

addData in interface OnlineInterpolator

Parameters:

f - the points to be interpolated

N

public int N()

Get the number of data points.

Returns:

the number of data points

getTable

public double[][] getTable()

Get a copy of the Neville table.

Returns:

a copy of the table

x

public double[] x()

Get a copy of the x's.

Returns:

a copy of x's.

get

public double get(int i,
                  int j)

Get the value of a table entry.

Parameters:

i - row index, counting from 0

j - column index, counting from 0

Returns:

the value of the table entry

evaluate

public double evaluate(double x)

Description copied from class: UnivariateRealFunction

Evaluate y = f(x).

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

x - x

Returns:

f(x)