Numerical Method20755 marksNumerical: Gauss Seidel methodGauss-Seidal Method
Solve the following set of equations using Gauss Seidel method.
Solve the following set of equations using Gauss Seidel method.
$$ \begin{aligned} x + 2y + 3z &= 4 \ 6x - 4y + 5z &= 10 \ 5x + 2y + 2z &= 25 \end{aligned} $$
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System of equations: $$x + 2y + 3z = 4 \quad \cdots (1)$$ $$6x - 4y + 5z = 10 \quad \cdots (2)$$ $$5x + 2y + 2z = 25 \quad \cdots (3)$$ Initial guess (standard): $x^{(0)} = y^{(0)} = z^{(0)} = 0$. To apply Gauss-Seidel we solve equation $(i)$ for $x$, $(j)$ for $y$, $(k)$ for $z$. To improve the ...