R: NEWS file for the minimaxApprox package

NEWS	R Documentation

NEWS file for the minimaxApprox package

So long as the package remains in its experimental development state—noted by a 0 major version—the API may change without incrementing the major version. Please read these development notes carefully. Breaking changes will be prefaced by “Breaking:”.

One unit test adjusted to pass on Professor Ripley's OpenBLAS test machine which has different tolerances than the standard twelve on CRAN, six on Github, three on R Win Builder, and the one on R Mac Builder.

Breaking: Analysis now uses the Chebyshev polynomials of the first kind, T_k, as the default basis instead of the monomials, x^k. Monomials can still be used by passing the appropriate basis parameter.
The internal functions underlying the Chebyshev polynomial calculations were ported to C for speed.

Breaking: Changed names in return object. What was Basis is now Extrema. The basis parameter is now used to capture whether monomials or Chebyshev polynomials should be/were used.
Breaking: User-facing functions now have basis parameter to determine which basis to use; see appropriate help files. Parameter positions have thus changed.
The print, plot, and coef methods were updated to recognize or allow basis selection.
The print method now shows 14 digits for the convergence ratio by default.
Internal code was streamlined and tolerances were tightened.
Updated documentation for new functionality.
The C files were split and header files created to keep Chebyshev and Horner code seperate from each other.

Breaking: More descriptive names in return object. See the Value section of help("minimaxApprox") for details.
Breaking: When using relative error for convergence and one of the basis points has a functional value of 0, instead of stopping with an error, the algorithm will perturb that basis point by 1e-12 in the appropriate direction and proceed with a warning.
Breaking: Forced convergence to look only at the ratio if the difference between tested values is \le .Machine$double.eps.
Breaking: Increased default for conviter from 10 to 30 as tests on some values now need more iterations to acheive ratio convergence given a distance \le .Machine$double.eps.

Refactored ‘README’ to split out security and contributions wordings to their own respective files and link the citation to the file on CRAN.
Changed some tests to be more acceptable for CRAN.

Test for calculating polynomial of degree n + 1 when one of degree n fails, while passing both R Mac Builder and Github's Mac platform, failed on CRAN's testbed. So test is no longer run for Mac on CRAN.

When the polynomial algorithm fails with a singular matrix error for degree n, it will now look for a polynomial of degree n + 1. If found, and the contribution of that coefficient is less than the new option tailtol (default 1e-10), it will return the found polynomial without the uppermost coefficient—which is effectively 0. It will message the user to that effect. Passing NULL skips the test. (see Issue 2 with thanks to Hans W. Borchers).
New option ztol which acts similarly to zapsmall in that it will zero out coefficient values—both polynomial and rational—whose contributions are \le ztol at each step of the iteration. The default, NULL, skips the test.

Ported Compensated Horner Scheme algorithms to C for speed. The algorithms are now roughly 10x faster.
Changed linear solution algorithm to use qr.solve when the default solve fails with a singular matrix issue. This may allow for higher degree polynomials in certain cases.
Breaking: Changed name of ‘round’ parameter in print method to ‘digits’ to prevent any confusion with base function round.
Updated unit tests.
Cleaned up and updated some documentation and various messages.
Tightened tolerances and cleaned up some internal functions.
Added ‘LICENSE’ to ‘.Rbuildignore’ and removed from ‘DESCRIPTION’ as suggested on R-pkg-devel.

Internal polynomial evaluations now uses Compensated Horner Scheme of Langlois et al. (2006) for increased precision and stability.
Clarified some error messages.

Remove one test which fails on M1 Mac (thanks to Professor Brian Ripley) and PowerPC (Issue 1; thanks to Sergey Fedorov) due to it returning a singular matrix where on Linux and Windows it does not.