Cubic Interpolation Spline

[tony21248772]

Hi,

I have a question on the setup of the tridiagonal system in the cubic
interpolation (under the choice 'Spline' for derivative approximation. The
tridiagonal system looks a bit different from the one suggested in the
literature. In particular, the middle components of the vector tmp_, the
right hand side vector of tridiagonal system, are caculated as:

            std::vector<Real> dx(n_-1), S(n_-1);

            for (Size

<http://quantlib.sourcearchive.com/documentation/1.1-1/namespaceQuantLib_af4cc4ef40b52c17cc455ead2a97aedb3.html#af4cc4ef40b52c17cc455ead2a97aedb3>
i=0; i<n_-1; ++i) {
dx[i] = this->xBegin_[i+1] - this->xBegin_[i];
S[i] = (this->yBegin_[i+1] - this->yBegin_[i])/dx[i];
}

            // first derivative approximation
            if (da_==CubicInterpolation::Spline

{
TridiagonalOperator
for (Size
=1; i<n_-1; ++i) {
L.setMidRow(i, dx[i], 2.0*(dx[i]+dx[i-1]), dx[i-1]);
tmp[i] = 3.0*(dx[i]*S[i-1] + dx[i-1]*S[i]);
}

Following the literature
L.setMidRow(i, dx[i-1], 2.0*(dx[i]+dx[i-1]), dx[i]);
tmp[i] = 3.0*(S[i] - S[i-1]);

Am I missing something here? Or any reference you can point me to
which derive what Quantlib implements?

Thanks,

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[lballabio]

I'm no longer sure, but it might be based on Numerical Recipes in C++?

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