Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix

When a function $f(x)$ is holomorphic on an interval $x \in [a, b]$, its roots on the interval can be computed by the following three-step procedure. First, approximate $f(x)$ on $[a, b]$ by a poly...

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