(RA15) The Weierstrass Approximation Theorem

In this video, we explore the application of continuous function approximation. We begin by exploring how to approximate functions with step functions, piecewise linear functions, piecewise quadratic functions, and generalize this to an arbitrary nth degree polynomial via the Weierstrass approximation theorem. We also introduce the Bernstein approximation theorem which gives us a procedural method for approximating continuous functions on [0, 1], for which we can then map back to the original domain if desired.

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For the matrix at around 23:00, the determinant should come out to about -0.97, and the coefficient vector should come out to:

(a, b, c) ~= (-0.3357, 1.1640, 0)