FeynmanKac.GetSplineCoefficients Method

FeynmanKacGetSplineCoefficients Method

Returns the coefficients of the Hermite quintic splines that represent an approximate solution of the Feynman-Kac PDE.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public double[,] GetSplineCoefficients()

Public Function GetSplineCoefficients As Double(,)

public:
array<double,2>^ GetSplineCoefficients()

member GetSplineCoefficients : unit -> float[,]

Return Value

Type: Double
A double matrix of dimension (tGrid.Length+1) by (3*xGrid.Length) containing the coefficients of the Hermite quintic spline representation of the approximate solution for the Feynman-Kac PDE at time points 0, tGrid[0],...,tGrid[tGrid.Length-1]. Setting ntGrid = tGrid.Length and nxGrid = xGrid.Length the approximate solution is given by

$f(x,t) = \sum_{j=0}^{3*\text{nxGrid}-1}y_{ij}\beta_j(x) \; \mbox{for} \; t=\text{tGrid}[i-1], i=1,\ldots,\text{ntGrid}.$

The representation for the initial data at t=0 is

$p(x) = \sum_{j=0}^{3*\text{nxGrid}-1} y_{0j}\beta_j(x)\,.$

The (ntGrid+1) by (3*nxGrid) matrix

$(y_{ij})_{i=0,\ldots,\text{ntGrid}}^{j=0,\ldots,3*\text{nxGrid}-1}$

is stored row-wise in the returned array.

Remarks

The ComputeCoefficients method must be invoked first before invoking this method. Otherwise, the method throws an InvalidOperationException exception.

Reference

FeynmanKac Class

Imsl.Math Namespace