minimaxapprox vs Rho

minimaxapprox computes minimax polynomial and rational approximations to functions via the Remez exchange algorithm. Version 0.6.0 is a correctness release of unusual depth: the exchange was redesigned after two structural defects were found that let it converge to a reference-local fixed point that is not the global minimax, with no warning. The worked example in the notes has atan on [0,3] at degree 3 reporting an expected error 1.8 times smaller than the returned approximation's true maximum error.

The redesign changes what drives the algorithm: roots are now located across the whole interval from an oversampled grid rather than only between consecutive reference points, each sign region takes its search direction from the error's own sign instead of a mechanically alternated schedule, and endpoints are always retained as exchange candidates. Around that sit a cluster of fixes with the same signature — a stagnation check tested in only one direction, a missing abs() in a coefficient test, ztol applied on the monomial scale when Chebyshev was requested — each one a silent wrong answer rather than a crash. Conditioning on ranges far from [-1,1] was also addressed, at the cost of a breaking change.

Nearly every fix here came from auditing places where the package trusted its own structure instead of measuring the error curve, so the next release most likely continues that audit into the rational-approximation path rather than adding features.