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I've just started reading about Tikhonov Regularization. Would someone please help with a simple numerical example of a case where regularization matrix of the form of a second order finite difference (tridiagonal matrix with 1,-2 and 1 at appropriate places) can be useful.

I'm guessing curve fitting might be a simple use case. But need a bit of help to understand exact usage.

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    $\begingroup$ My answer here is one example. Curve fitting would also be a reasonable example. In that context a curvature-based penalty would be a way to essentially get a smoothing spline (2D case here). $\endgroup$
    – GeoMatt22
    Dec 18 '16 at 3:54

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