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The theory of polar forms of polynomials is used to provide sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic stability radius), to be inscribed in the stability region of an explicit Runge–Kutta method. The bounds on the absolute stability radius are derived as a consequence of Walsh’s coincidence...
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete $$L_2$$ L 2 -norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted...
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