91Ó°ÊÓ

Apart from mistakes in entering or reading data, the two main sources of error in numerical analysis are truncation error and rounding error. The cumulative effect of such errors can make the final result suspect. Give illustrations of truncation and rounding errors.

Use the Crout method to solve the system $$ \begin{aligned} 2 \mathrm{x}_{1}-\mathrm{x}_{2} &=6 \\ -\mathrm{x}_{1}+3 \mathrm{x}_{2}-2 \mathrm{x}_{3} &=1 \\ -2 \mathrm{x}_{2}+4 \mathrm{x}_{3}-3 \mathrm{x}_{4} &=-2 \\ -3 \mathrm{x}_{3}+5 \mathrm{x}_{4} &=1 \end{aligned} $$

Use the Gauss-Seidel method to solve the following linear system: $$ \begin{aligned} &10 \mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}=15 \\ &\mathrm{x}_{1}+10 \mathrm{x}_{2}+\mathrm{x}_{3}=24 \\ &\mathrm{x}_{1}+\mathrm{x}_{2}+10 \mathrm{x}_{3}=33 \end{aligned} $$

Construct a flow chart for the simplex method of linear programming.

Construct a flow-chart for solving the set of simultaneous linear equations \(A X=b\) by finding the inverse of the coefficient matrix.

Construct a flow-chart for inversion of a matrix using the Gauss-Jordan method.