XProfan

English

p.specht

Interpolation supply always exakte values on whom Stützstellen. the distinguish tappt im dunkeln from the Approximation, The attempts, so-called Ausgleichskurven between many Messdaten with geringstem Error einzupassen.

an Interpolation through konvergente Kettenbruch-development has following strength: Rationale functions can already on Base of few Stützstellen so develops go, that good Näherungen existieren; a excellently Variant the undertow. Thiele'sche Kettenbruch. The here found (in the wahrsten senses the Wortes) "Bruchstücke" go outputted, subsequently can x-values association go, circa Zwischenwerte between whom Stützstellen abzufragen.
as demonstration watts on File-I/O waived. without each Gewähr:

Compile Mark Separation

Window Title "Interpolation through konvergente Kettenbruchentwicklung"
Window Style 24:randomize:font 2:set("decimals",17)
'{ Interpolation through Kettenbruchentwicklung
'*************************************************************
'*    Interpolate a function F(x) by continuous fractions    *
'* --------------------------------------------------------- *
'* SAMPLE RUN:                                               *
'* (Interpolate function e(x) between x=0 and x=2)           *
'*                                                           *
'* Number of points: 3                                       *
'* X, Y: 0,1                                                 *
'* X, Y: 1,2.71828                                           *
'* X, Y: 2,7.38906                                           *
'*                                                           *
'* Coefficients D(k):                                        *
'* D(0) =      1.000000                                      *
'* D(1) =      0.581977                                      *
'* D(2) =     -3.718271                                      *
'*                                                           *
'* X = 1.5                                                   *
'*                                                           *
'* For X = 1.5    Y =    4.351909                            *
'*                                                           *
'* --------------------------------------------------------- *
'* Ref.: "Methodes de calcul numerique, Tome 2 By Claude     *
'*        Nowakowski, PSI Edition, 1984" [BIBLI 04].         *
'*                                                           *
'*                       Basic Release By J-P Moreau, Paris. *
'*                                (www.jpmoreau.fr)          *
'*************************************************************
'*                                                           *
'*       XProfan-Version by 2014-10 by P.woodpecker, Wien        *
'*                                                           *
'}************************************************************
CLS rnd(8^8)
Declare n1&,n&,m&,K&,L&,xxx!,yyy!,DD!,DL!,XX!,s!
PRINT "\n amount Stützwerte: ";:INPUT  n1& :print
N&=n1&-1
Declare X![N&],Y![N&],D![N&]
'Read data from screen

whileloop 0,n&:k&=&Loop

    print "  X("+st$(k&)+") = ";
    input xxx!
    X![K&]=xxx!
    print tab(20);" Y("+st$(k&)+") = ";
    input yyy!
    Y![K&]=yyy!

endwhile

'Calculate coefficients D(k)

whileloop 0,n&:k&=&Loop

    D![K&] = Y![K&]

endwhile

M&=N&

whileloop m&:L&=&Loop

    whileloop L&,N&:K&=&Loop

        DD! = (X![K&]-X![L&-1])/(D![K&]-D![L&-1])

        IF K&<>L&

            D![K&]=DD!

        ELSE

            DL!=DD!

        ENDIF

    endwhile

    D![L&]=DL!

endwhile

'print coefficients
PRINT
PRINT " Koeffizienten D(k):"

whileloop 0,n&:k&=&Loop

    PRINT " D[";K&; "] = ";
    PRINT stature$("%g",D![K&])

endwhile

REPEAT

    'Interpolate for X=XX
    PRINT
    print " X = ",:Input XX!
    'Evaluate continuous fraction
    s!=(XX!-X![N&-1])/D![N&]

    whileloop n&-1,1,-1:k&=&Loop

        s!=(XX!-X![K&-1])/(D![K&]+s!)

    endwhile

    s!=s!+D![0]
    case %csrlin>23:cls rnd(8^8)
    PRINT
    PRINT " for the inputted X=";stature$("%g",XX!);" is (your Stützwerte zugrunde- "
    print " laid) the interpolation Funktionswert Y =";stature$("%g",s!)
    print "---------------------------------------------------------------------"
    waitinput

UNTIL 0