Re: [Quantlib-dev] cubic interpolation

[Luigi B. <lui...@gm...>]

Apologies for the delay; I didn't find the time to go back and check the
math. I see from <
http://www.wilmott.com/messageview.cfm?catid=4&threadid=98075&forumid=1>
that you solved the issue, though. Is this correct?

Luigi


On Thu, Jan 29, 2015 at 5:59 AM, Sk Wong <sk...@gm...> wrote:

> 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
>
>
>
>
>
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