Numerical Methods20795 marksNumerical: Gauss-Seidel methodGauss-Seidel iteration method
Solve the following system of linear equations using Gauss-Seidal method.
Solve the following system of linear equations using Gauss-Seidal method.
$$\begin{aligned} 10x + y + z &= 12 \ 2x + 10y + z &= 13 \ 2x + 2y + 10z &= 14 \end{aligned}$$
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System of linear equations: $$10x + y + z = 12 \quad \cdots (1)$$ $$2x + 10y + z = 13 \quad \cdots (2)$$ $$2x + 2y + 10z = 14 \quad \cdots (3)$$ Initial approximation: $x^{(0)} = y^{(0)} = z^{(0)} = 0$ Row 1: $10 \geq 1+1$; Row 2: $10 \geq 2+1$; Row 3: $10 \geq 2+2$. The matrix is diagonally domi...