VB で連立一次方程式を解く(ヤコビの反復法)

例として
$9x+2y+z+u=20$
$2x+8y-2z+u=16$
$-x-2y+7z-2u=8$
$x-y-2z+6u=17$
を考える.
この方程式を上から順に対角線上の変数について解くと
$x=(20-2y-z-u)/9$
$y=(16-2x+2z-u)/8$
$z=(8+x+2y+2u)/7$
$u=(17-x+y+2z)/6$
となる.
$x,y,z,u$ に適当な値を入れて右辺を計算し、
得られた値を新たな $x,y,z,u$ として、計算を繰り返す.
漸化式で書くと
$x_{n+1}=(20-2y_n-z_n-u_n)/9$
$y_{n+1}=(16-2x_n+2z_n-u_n)/8$
$z_{n+1}=(8+x_n+2y_n+2u_n)/7$
$u_{n+1}=(17-x_n+y_n+2z_n)/6$

Option Explicit

Module VB1001
    Private Const N As Integer = 3
    
    Public Sub Main()

        Dim a(,) As Double = {{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}
        Dim b()  As Double = {20,16,8,17}
        Dim c()  As Double = {0,0,0,0}

        'ヤコビの反復法
        jacobi(a,b,c)

        Console.WriteLine("解")
        For i As Integer = 0 To N
            Console.Write(string.Format("{0,14:F10}{1}", c(i), vbTab))
        Next
        Console.WriteLine()
    End Sub
    
    Private Sub jacobi(a(,) As Double, b() As Double, x0() As Double)
        Do While(True)
            Dim x1() As Double = {0,0,0,0}
            Dim finish As Boolean = True
            For i As Integer = 0 To N
                x1(i) = 0
                For j As Integer = 0 To N
                    If j <> i Then
                        x1(i) += a(i,j) * x0(j)
                    End If
                Next

                x1(i) = (b(i) - x1(i)) / a(i,i)
                If (Math.Abs(x1(i) - x0(i)) > 0.0000000001) Then finish = False
            Next

            For i As Integer = 0 To N
                x0(i) = x1(i)
                Console.Write(string.Format("{0,14:F10}{1}", x0(i), vbTab))
            Next
            Console.WriteLine()

            If finish Then Return
        Loop
    End Sub
End Module

  2.2222222222    2.0000000000    1.1428571429    2.8333333333
  1.3359788360    1.3759920635    2.8412698413    3.1772486772
  1.2477219283    1.9791666667    2.6346371882    3.7870921517
  1.0688819252    1.8733422960    2.9686056521    3.8334531858
  1.0501396189    1.9957492835    2.9260675555    3.9569452792
  1.0139431776    1.9743638243    2.9936469635    3.9662907960
  1.0101482880    1.9991395970    2.9850360597    3.9912857623
  1.0028221093    1.9948112226    2.9987141438    3.9931772381
  1.0020540192    1.9998258539    2.9969712901    3.9982362335
  1.0005711965    1.9989497885    2.9997397420    3.9986190691
  1.0004157346    1.9999647527    2.9993869874    3.9996430127
  1.0001156105    1.9997874366    2.9999473236    3.9997204988
  1.0000841449    1.9999928659    2.9998759259    3.9999277456
  1.0000233996    1.9999569771    2.9999893383    3.9999434288
  1.0000170310    1.9999985561    2.9999748873    3.9999853757
  1.0000047361    1.9999912921    2.9999978421    3.9999885500
  1.0000034471    1.9999997077    2.9999949172    3.9999970400
  1.0000009586    1.9999982375    2.9999995632    3.9999976825
  1.0000006977    1.9999999408    2.9999989712    3.9999994009
  1.0000001940    1.9999996433    2.9999999116    3.9999995309
  1.0000001412    1.9999999880    2.9999997918    3.9999998787
  1.0000000393    1.9999999278    2.9999999821    3.9999999051
  1.0000000286    1.9999999976    2.9999999579    3.9999999755
  1.0000000079    1.9999999854    2.9999999964    3.9999999808
  1.0000000058    1.9999999995    2.9999999915    3.9999999950
  1.0000000016    1.9999999970    2.9999999993    3.9999999961
  1.0000000012    1.9999999999    2.9999999983    3.9999999990
  1.0000000003    1.9999999994    2.9999999999    3.9999999992
  1.0000000002    2.0000000000    2.9999999997    3.9999999998
  1.0000000001    1.9999999999    3.0000000000    3.9999999998
  1.0000000000    2.0000000000    2.9999999999    4.0000000000
  1.0000000000    2.0000000000    3.0000000000    4.0000000000
解
  1.0000000000    2.0000000000    3.0000000000    4.0000000000

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VB で連立一次方程式を解く(ヤコビの反復法)

参考文献