Tag Archives: Linearization

Linearisation bounds for smooth mutlivalued functions

By psopasakis on June 25, 2016 | Leave a comment

How far is a function $f$ from its linearisation? Typically, one would assume that $f$ is twice continuously differentiable and use the following second-order version of the mean value theorem:

$f(y) = f(x) + \langle J f(x),y-x\rangle + \int_0^1 (1-\tau) (y-x)'\nabla^2 f(x+\tau (y-x))(y-x)\mathrm{d}\tau$

This is typically used in the context of linearisation of nonlinear dynamical systems as in [Sec. 2.5.1.3, 1]. The requirement that $f$ is twice continuously differentiable, can, however, be reduced to $f$ being continuously differentiable with Lipschitz gradient. Continue reading →

Posted in: Analysis | Tagged: Calculus, Linearisation, Linearization, Multivalued mean value theorem, MVT

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Linearisation bounds for smooth mutlivalued functions

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