Two compact numerical algorithms are explored for embedded and scientific computing: quadratic extremum interpolation and Chandrupatla's root-finding method. Quadratic interpolation fits a parabola to three sampled points around a waveform peak, achieving cubic error scaling with timestep — a significant improvement over the quadratic scaling of raw sample maxima. The technique requires smooth, well-sampled data to work reliably. Chandrupatla's 1997 method is presented as a simpler alternative to Brent's method for bracketed root-finding, combining bisection with inverse quadratic interpolation using a straightforward switching criterion. Python implementations and convergence comparisons against scipy's brentq are provided, showing Chandrupatla converges comparably or faster on flat/multiple-root functions.
