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2 users thanked CBG for this useful post.
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on 12/02/2020(UTC), on 13/02/2020(UTC)
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Rank: Advanced Member Groups: Registered
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Originally Posted by: Jean Giraud Thanks Carlos ... works well. More from Maple ... Jean
Hola Jean Thank you very much for your examples, they have helped me to correct a fault that was presented in the ACOS (X) function, where the value of "Phi () / 2" was not included. I have merged all the algorithms in a single function for ease of use. All the examples you provided work perfectly with the algorithm for the conversion of function to a continuous function. SMATH STUDIO VERSION 7251, DOES NOT ACCEPT THE ACOS (X), ASIN (x) AND ATAN (X) FUNCTIONS FOR MAPLE, GIVING THE "EMPTY STACK" ERROR. Continuous_Fraction_algorith_SS7251.sm (77kb) downloaded 18 time(s). Continuous_Fraction_algorith_SS6179.sm (78kb) downloaded 17 time(s).Best Regards Carlos
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Originally Posted by: CBG SMATH STUDIO VERSION 7251, DOES NOT ACCEPT THE ACOS (X), ASIN (x) AND ATAN (X) FUNCTIONS FOR MAPLE, GIVING THE "EMPTY STACK" ERROR. Maybe Viacheslav can doctor the sick Maple. Few more in there Carlos ... Jean Symbolic Convert Parfrac Primary FNCTS.sm (102kb) downloaded 19 time(s).
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In his book, C.T. Fike mentions few system having implemented the continued fraction for some functions [IBM 360 ...], 1965. From there, the next step was to economize the CF ... from which the J_Fraction originates. By same token, minimax rational fractions to replace the CF. Those style rational fraction aren't very numerically stable. Then the Padé normalized rational fractions origin, more stable. Built-in Microsoft functions are Padé [AFAIK], normalized 15 D. More decimals can be obtained from Chebyshev, rated 25 D, only available in Main Frames.
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Originally Posted by: CBG I have merged all the algorithms in a single function for ease of use.
All the examples you provided work perfectly with the algorithm for the conversion of function to a continuous function.
Superb, Carlos ... saved, thanks. Continued fractions are pure fascination. They date back long time ago from Mesopotamians, brought back by the Templars. As a matter of fact, the first Crusade never came back, and bypassed Jerusalem. Wallis [Newton's teacher] developed a method to compute top/down. It is certainly coded this way in modern computing machinery [advanced CAS]. Damned hard work to compute in Excel and more not CAS. If you were with Mathcad/Mathsoft before Smath, there is "confrac" work sheet from Jesper Gundermann [Danish]. He also provided the BigNumber engine to display > 15 decimals that imitate Mathcad symbolic. In his book, F.B. Hildebrand you will find an interesting chapter. It became the source of approximating data sets that delighted you so much, and elevates common Engineering works Hola ! carlos ... Jean
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Rank: Guest
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Joined: 04/07/2015(UTC) Posts: 6,868 Was thanked: 980 time(s) in 808 post(s)
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Originally Posted by: Jean Giraud ... in my old style Under the hood, there is a "Big Number" red issue, solved manually, not exposed in the document. Otherwise: 1/1 happy ... Publishing style. Inst_ISA [kPa] solve NASA altitude [20200215] Copy.sm (106kb) downloaded 17 time(s).
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