Two additional articles online: Minimax & Sudoku



#6

Hi all,

    I'm taking my summer vacations in a few days, so I'll be
    unable to access this forum or process e-mails till my eventual return a month or so from now. As a 'departing gift' I've put two of my recent Datafile
    articles on line, in PDF format, for you to freely download
    from my HP calc site. Both 'brief abstracts' follow:

    Minimax Polynomial Fit

      "By definition, the minimax polynomial is the approximating polynomial which has the smallest maximum deviation from the true function. Thus, we’re minimizing ABS(P(x)-f(x)) instead of (P(x)-f(x))2 ...

      MMAXPOLY is a 50-line (w/o comments) program I’ve written to compute minimax polynomial approximations to any given set of data points. You can enter the data points directly from the keyboard, you can specify a generating function which will be evaluated in a given range to automatically generate the dataset, or you can read the dataset from a file. In the first two cases, the whole dataset can be stored in a file, for later retrieval and possibly further fitting or processing ...

      MMAXPOLY allows the user to either specify a particular degree for the minimax polynomial, or else to give a maximum absolute error to be met, in which case it will iteratively compute a series of minimax polynomials for the given dataset, starting from degree 1 and incrementing it until either the maximum absolute error is equal or less than the one specified, or the degree is already N-1 (where N is the number of points in the dataset), which, rounding errors notwithstanding, would necessarily result in an exact fit (maximum error = 0 ) ...

      Minimax polynomial fitting is an incredibly powerful technique to add to one’s own data-fitting arsenal. Though the internal details are complex enough and it does require a lot of computing muscle when compared to other well-known strategies such as Least Squares, the final reward is the improved accuracy it provides for any given degree or, conversely, the least possible degree for any given accuracy. It may take longer to compute the minimax polynomial, but typically you do that exactly once, then evaluate the resulting polynomial many times, which, being of lower degree than the ones obtained by other methods, will then execute faster and thus result in time savings in the long run."

    Sudoku Solver’s Sublime Sequel

      "This very small program, just 45 lines and well under 2 Kbytes of code (1898 bytes), will recursively solve any solvable Sudoku puzzle, fast. Carefully crafted, comprehensive 15-puzzle Test Suite included, which apart from showing this solver's performance in action can also be useful to you in order to test other solvers or even you own Sudoku abilities."

    That's all, I hope you enjoy the articles. Happy summer vacations to all of you and
Best regards from V.


Edited: 27 July 2006, 3:57 a.m. after one or more responses were posted


#7

Valentin,

I had already appreciated your articles on the Datafile, so

"simply" accept my best wishes for your holidays.

Hear you soon on the Forum!

Take care.

Giancarlo

#8

Rest and get ready for our questions of September and beyond...

Good holidays, Valentin!

-- Antonio

#9

Cool article. Thanks!

Where are you going for your vacation?

Namir


#10

Hi, Namir:

Namir posted:

"Cool article. Thanks!
Where are you going for your vacation?"

    Thanks for your interest, I'm glad that you like it. I'll be staying at an extremely small (summer population: 100, winter population: 20) village in a valley amid mountains in northern Spain.

    It's the ideal place to absolutely rest, relax, and disconnect from work, but (fortunately ? sadly?) there's no way to access internet, e-mail, and just the one cellular phone. I'm gonna certainly miss this forum, but will have time to concoct several S&SMC and HP-15C Mini-challenges, as well as a new article or two :-)

    I'm departing right now, see you all next September or so.

Best regards from V.

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