[Quantlib-dev] cubic interpolation

[Sk W. <sk...@gm...>]

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
<http://quantlib.sourcearchive.com/documentation/1.1-1/classQuantLib_1_1CubicInterpolation_a6897ea07ce6993b4df934091a3723d28.html#a6897ea07ce6993b4df934091a3723d28aaa6b6cbb8010b02172412742c21ce2d7>)
{
                    TridiagonalOperator
<http://quantlib.sourcearchive.com/documentation/1.1-1/classQuantLib_1_1TridiagonalOperator.html>
L(n_);
                    for (Size
<http://quantlib.sourcearchive.com/documentation/1.1-1/namespaceQuantLib_af4cc4ef40b52c17cc455ead2a97aedb3.html#af4cc4ef40b52c17cc455ead2a97aedb3>
i=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, one instead has (e.g. see Eq. 6.62 in
Piterbarg-Andersen book V1 Chapter 6 Appendix):

tmp[i] = 6.0*(S[i] - S[i-1]);


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



Thanks,

SK