Linear Approximation: Estimating Both Function Values and Input Values
Introduction Linear approximation is generally introduced as a method of estimating the value of a function near a known point. However, the…
linear approximation
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Why Newton’s Method Converges Quadratically: The Hidden Connection Between Linear, Quadratic, and Higher-Order Approximations
Introduction One of the most interesting features of Newton’s method is that it uses a linear approximation to achieve quadratic convergence. At…
Linear Approximation and Concavity: How the Second Derivative Sharpens Your Estimates
Tangent lines are one of the quickest ways to estimate a function near a known point. But a tangent line is only…
Linear Approximation: Estimating Values with a Tangent Line
Some values are hard to compute by hand, like √4.1. Linear approximation lets you estimate them quickly using the tangent line of…
