Linearization of function of 2 variables, Matlab: linearization error analysis, Hessian eigenvalues

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 09:04

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Summary:

This video is a continuation of the video [linmiso1EN]. Here, the accuracy of the linearization is evaluated numerically at a certain point (incremented from the operating point), and then a map (contour) of the approximation error is drawn.

Obviously, near the origin, the difference between the original function and the linearized approximation is dominated by the degree 2 terms of the Taylor expansion, so the properties of the Hessian (matrix of second derivatives) allow us to estimate the linearization error and its properties near the operating point: all eigenvalues of the same sign indicate “ellipsoidal” contours of the error, eigenvalues of different sign would indicate “hyperbolic” type contours (not the case in the example here).

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