XProfan

English

p.specht

The Gauss-Seidel-Iteration is a zyklisches take action to Solution linearer Gleichungssysteme (LGS) the general shape A*x = b.
These can schrittweise solve, because one multiple rechnet:
x(new) = x(old) - Korr, with Korrekturvektor Korr = A*x(old) - b

it deals itself means circa a Fehlerrückkopplung. eachone Passage correct the Result a little bit. one begins thereby with geratenen Values, and something Happiness comes one Error very near zero out.

The Gauß-Seidel-Iteration is Specifically appropriate to badly konditionierte Gleichungsysteme (the are such, with them itself Rundungs- and Binärübersetzungsfehler mutual join would). tappt im dunkeln reacted too less sensitive on fehlerbehaftete Koeffizienten as the Gauß-take action. Natürlicher disadvantage of Iterationsverfahren is, that the Rechenzeit vastly larger is as with direct Algorithms.

Fehlermeldungen should improved go, because the case "Singuläre Matrix" lying with Division through zero namely not always to. it was however meaningfully, at least this Error once abzufangen.

Compile Mark Separation

Window Title "LGS-Solution through Gauß-Seidel-Iteration"
' fountain: https://www.rhirte.de/vb/gleichsys.htm#seidel
' from Visual Basic in XProfan 11.2a Translated of
' P. woodpecker 2012-04. Demoware! No How always geartete Liability,
' usage solely on own risk the Anwenders!
'
' TESTMATRIX DEFINIEREN:
Var n&=4
Var e!=val("1e-9")
Declare A![n&,n&+1],x![n&],it$
'            Koeffizienten                 +  rights Page:
A![1,1]=1 :A![1,2]=0 :A![1,3]=0 :A![1,4]=0 :  A![1,5]=10' = b1
A![2,1]=0 :A![2,2]=1 :A![2,3]=0 :A![2,4]=0 :  A![2,5]=20' = b2
A![3,1]=0 :A![3,2]=0 :A![3,3]=1 :A![3,4]=0 :  A![3,5]=30' = b3
A![4,1]=0 :A![4,2]=0 :A![4,3]=0 :A![4,4]=1 :  A![4,5]=40' = b4
Start:
Declare xp![n&],R!,s!,T!,i&,j&,num&

WhileLoop n&:i&=&Loop

    x![i&] = 5' Startvektor with of/ one first Ausgangslösung

EndWhile

Repeat

    WhileLoop n&

        i&=&Loop
        s!=0

        WhileLoop i&-1

            j&=&Loop
            s!=s!+A![i&,j&]*xp![j&]

        EndWhile

        T!=0

        WhileLoop i&+1,n&

            j&=&Loop
            T!=T!+A![i&,j&]*X![j&]

        EndWhile

        if A![i&,i&]=0

            print " Singuläre Matrix!"
            it$="sing"
            BREAK

        Endif

        xp![i&]=(A![i&,n&+1]-s!-T!) / A![i&,i&]

    EndWhile

    case it$="sing":break
    s!=0

    WhileLoop n&:i&=&Loop

        R!=X![i&]-xp![i&]
        s!=s!+ R!*R!
        X![i&]=xp![i&]

    EndWhile

    num& = num& + 1

Until Sqr(s!/(n&-1)) < e!

Case it$<>"":Goto "Stop"
' spending:
print "\n Result found in ";num&;" Durchläufen:"

WhileLoop n&

    i&=&Loop
    print " x"+st$(i&)+" = ";x![i&]

EndWhile

Stop:
print
WaitInput
End