Robust plotting of generalized lemniscates
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Weierstrass-type approximation theorems with Pythagorean hodograph curves
Computer Aided Geometric Design
Computing the Minkowski Value of the Exponential Function over a Complex Disk
Computer Mathematics
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An n-th Minkowski root \math of a given complex set A is defined by the property \math, i.e., the set of all products of n independently chosen values from \math is identical to A . Hence, the n-th Minkowski power of \math yields the original set A . Minkowski root extractions are fundamental operations in the Minkowski geometric algebra of complex sets: depending on the nature of A , subtle issues concerning the existence, uniqueness, and minimality or maximality of \math may arise. For a domain A with a smooth boundary that is strictly logarithmically convex, we show that each connected component of the 驴ordinary驴 root \math is a Minkowski n-th root. \math has a more intricate structure, however, when \math has logarithmic inflections. For example, if A is a \math is (a single loop of) the 驴n-th order驴 ovals of Cassini or lemniscate of Bernoulli when \math or \math, respectively. But when 0 is in the interior of A, a composite curve (portions of the Cassini ovals and a higher-order curve) is required to describe \math .