Question

Consider the system of linear algebraic equations, in which the coefficients and the constants are known to the number of significant digits shown. 4.000y - 5.000z = -8.000 3.000x - 6.000y - 2.000z = -23.00 5.000x - 1.000y = 2.000 Write and execute VBA code to solve the system of equations with the Gauss-Seidel algorithm. Let the solution be considered to have converged when consecutive estimates for all three variables differ by less than l0.00001% l.

Answer 1

VBA code

4.000y - 5.000z = -8.000
3.000x - 6.000y - 2.000z = -23.00
5.000x - 1.000y = 2.000

simple matrix formula A*x = B

A = [ 0 , 4 , - 5 ; 3 , - 6 , -2 ; 5 , -1 , 0 ]

B = [ - 8, -23, 2 ]

you solve this equation, you'll find x = 1, y = 3, z = 4 ; in terms of the matric.

So, C = [ 1 ; 3 ; 4 ]

Now with the help of Excel's worksheets alongside its MMULT and MINVERSE functions makes this easy. My problem is I'm needing to do this calculation inside a VBA function.

Dim A(0 To 2, 0 To 2) As Single
Dim B(0 To 0, 0 To 2) As Single
Dim X(0 To 0, 0 To 2) As Single

A(0, 0 ,0 ) = 0
A(1, 0 ,0 ) = 4
A(0, 1 ,0) = -5
A(0, 0, 1) = 3

A(1, 1, 0 ) = -6

A(1, 0 ,1) = -2

A(0 , 1 , 1 ) = 5

A( 1 , 1 , 1 ) = -1

B(0 , 0 , 0) = -8

B(0 , 1 , 0) = -23

B(1, 1, 1 ) = 2

Gauss-Seidel algorithm

4.000y - 5.000z = -8.000
3.000x - 6.000y - 2.000z = -23.00
5.000x - 1.000y = 2.000

To compare our results from the two methods, we again choose x⁽⁰⁾ = (0, 0, 0). We then find x⁽¹⁾ = (x₁⁽¹⁾, x₂⁽¹⁾, x₃⁽¹⁾) by solving

0 - 0 = -8.000
3.000x - 6.000y - 0z = -23.00
5.000x - 1.000y = 2.000

In this we will use eign value and eigh vetor mathode;

X = [ k1 , k2 , k3 ] ;

Now put the values accordingly