Polynoms.PolyCoeff Method

Overload List

#	Signature	Description
1	void PolyCoeff(TMtx Mtx, TVec Coeff)	Returns coefficients of the characteristic polynomial.
2	void PolyCoeff(TVec Roots, TVec Coeff)	Converts polynomial roots to coefficients.

Overload 1: void PolyCoeff(TMtx Mtx, TVec Coeff)

Returns coefficients of the characteristic polynomial.

#	Name	Type	Description
1	Mtx	TMtx	source TMtx
2	Coeff	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Returns coefficients of the characteristic polynomial: det( Mtx - Lambda * I ).

Examples

using Dew.Math;
using Dew.Math.Units;
using Dew.Math.Editors;

namespace Dew.Examples
{
    private void Example()
    {
        Vector Coeff = new Vector(0);
        Matrix A = new Matrix(0,0);
        A.SetIt(3,3,false, new double[] {1,  4, -1,
            2,  1,  5,
            3, -2,  0});
        Polynoms.PolyCoeff(A,Coeff);
        MtxVecEdit.ViewValues(Coeff,"Coefficients");
    }
}

See Also: Polynoms.PolyRoots

Overload 2: void PolyCoeff(TVec Roots, TVec Coeff)

Converts polynomial roots to coefficients.

#	Name	Type	Description
1	Roots	TVec	source TVec
2	Coeff	TVec	source TVec

Result: stored in self (calling object)

Remarks:

The PolyCoeff procedure converts polynomial roots to coefficients. The following scheme is used to construct a coefficients from the roots:

P(x) = coeff[0] x^n + coeff[1] x^(n-1) + ... + coeff[n] = (x - roots[0]) ... (x - roots[n-1])

n .. order of the polynomial

The length and complex property of the Coeff object are set automatically. The inverse to this routine is Dew.Math.Units.Polynoms.PolyRoots