Numerical Differentiation Options dialog box

 

Use this dialog box to specify the options for the numerical differentiation of data in preparation for another operation.

 

Refer to the Numerical Differentiation dialog box for additional information on this subject.

 

General Options

 

Method

Specifies the method that will be used to carry out differentiation.

 

Cubic Splines

Select this option to carry differentiation using interpolating cubic splines.

Refer to Cubic Spline Type and Spline End Conditions in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Difference Formula

Select this option to carry differentiation using difference formula.

 

Piecewise Polynomials

Select this optionates to carry differentiation using piecewise polynomials.

 

Polynomial Interpolation

Select this option to carry differentiation using polynomial interpolation.

 

Cubic Spline Type

Specifies the cubic spline that will be used for differentiation. Select one of the following:

 

Clamped Spline

Where the end-point conditions refer to the value of the first derivative of the series at its extreme points.

Refer to Complete Cubic Splines for additional information on this subject.

 

Natural Spline

Where the end-point conditions refer to the value of the second derivative of the series at its extreme points.

Refer to Natural Cubic Splines for additional information on this subject.

 

Third Derivative

Where the end-point conditions refer to the value of the third derivative of the series at its extreme points.

Refer to Splines With Specified End-Point Third Derivatives for additional information on this subject.

 

Not-a-Knot Spline

Where the third derivative of the spline function is continuous at the second and second-to-last nodes.

Refer to Not-a-knot Splines for additional information on this subject.

 

Difference

Specifies the type of difference formula that will be used for differentiation. Select one of the following:

 

Backward

Select this option to differentiate using the backward difference formula.

 

Central

Select this option to differentiate using the central difference formula.

 

Forward

Select this option to differentiate using the forward difference formula.

 

Spline End Conditions

Conditions for the first and last points will have different meanings depending on the selected Cubic Spline Type.

 

Start Point Condition

Type in this box the value of the condition of the first or start point of the series. For example, type a value of zero (0) for the first derivative of the first point of the series in relation to clamped splines to make the series appear as having extrema at this point.

 

End Point Condition

Type in this box the value of the condition of the last or end point of the series. For example, type a value of one (1) for the first derivative of the last point of the series in relation to clamped splines to make the series appear as increasing at this point.

 

Refer to Interpolating Cubic Splines for additional information on this subject.

 

Piecewise Polynomial Parameters

Specifies the parameters for calculating derivatives using interpolating piecewise polynomials.

 

Number of Points

Specifies the number of consecutive points used to solve each polynomial. Type in this box a value in the range of 3 through 16, or the length of the selected series if the latter is shorter than 16.

 

Center Point

Specifies the point number at every piece where the indicated derivatives are calculated. Type in this box a point number in the range of 1 through Number of Points.

 

 

Because of length constraints, the piece centering point may differ for the derivatives at the extreme points of a series. For example, if you choose 3 as the centering point of a 5 points piece segment, derivatives for the series points 1, 2, N-1, and N (N being the length of the series), must be computed at the piece points 1, 2, 4 and 5, respectively.

 

OK

Click this button to close the dialog box and save any changes you have made.

 

Cancel

Closes the dialog box and discards the specified options.