# Talk:Linearization

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## Fix

Can someone better at Wiki editing fix this? In the section "Linearization of a Function", at the end it says: "For x = a, f(a) is f(x) at a. The derivative of f(x) is f'(x), and the slope of f(x) at a is f'(a)." But the derivative, i.e., "f'(x)" is not displaying with the apostraphe. Also, I deleted the following line, which is actually a discussion and not an encyclopedic entry: "Instead of a linear function, perhaps, would x not be better approximated with polynomial? This can be accomplished via Taylor series. This is not the purpose of linearization though." Perhaps it could be stated instead as something like: "x can be approximated via Taylor series". —Preceding unsigned comment added by 70.165.109.56 (talk) 17:39, 15 September 2007 (UTC)

It doesn't make any sense! —Preceding unsigned comment added by 198.86.17.162 (talk) 15:44, 4 May 2009 (UTC)

## Good article

This article is good because it starts off with a laymen's explanation of what is going on. Only then does it get into more complicated stuff. Too many articles written in Wiki bypass this important step and go right to the high-level (elite) explanations..............good job. —Preceding unsigned comment added by 99.147.240.11 (talk) 13:49, 6 September 2010 (UTC)

## Article Inaccuracies

The intuition given by this article is fine, but the details are not correct. Not every continuous function is linearizable; the function must be once differentiable. (I wouldn't consider vertical tangents to be linearizations, but to me, that's a choice of convention.) A function is linearizable iff it has a linear approximation good to the second order; this precise definition should show up in the article in some form. The sentence about points that are "arbitrarily close" versus points that are "relatively close" is not precise. The idea of "local linearity" may be a helpful intuition, but it should not be substituted for a rigorous definition.

Sorry to point out problems without fixing them, but I won't be rewriting things here anytime soon. I wanted to note these issues for anyone who comes around before then. 140.114.81.55 (talk) 03:02, 22 October 2010 (UTC)

## Stability analysis and linearization justification

The section Stability analysis is not correct: 1) it should be considered sign of real parts of eigenvalues 2) negativeness of real part of all eigenvalues implies stability (in general case) only for autonomous systems (${\displaystyle F(t,x)=F(x)}$). Time-varying linearization requires additional justification (G.A. Leonov, N.V. Kuznetsov, Time-Varying Linearization and the Perron effects, International Journal of Bifurcation and Chaos, Vol. 17, No. 4, 2007, pp. 1079-1107) [1]Kuznetsov N.V. (talk) 17:30, 25 September 2011 (UTC)

## First line

I'm just trying to learn about this topic so I hesitate to question this, but shouldn't the first line read "linear approximation of a function?" If not, an explanation of why not would be helpful. — Preceding unsigned comment added by Southandros (talkcontribs) 15:38, 25 April 2013 (UTC)

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1. ^ G.A. Leonov, N.V. Kuznetsov (2007). "Time-Varying Linearization and the Perron effects". International Journal of Bifurcation and Chaos. 17 (4): 1079–1107. doi:10.1142/S0218127407017732.