Perform four iterations (rounded to four decimal places) using
(i) Jacobi Method and
(ii) Gauss-Seidel method,
for the following system of equations
. The exact solution is (1, 2, 3)T. Which method gives better approximation to the exact solution?
We are given the linear system: $$ \begin{aligned} 5x_1 - 5x_2 - x_3 &= -8 ______ ______ ________ ____ _____.
_____ _____ _________ _____ _____ _______ _________ _________ _____ _________.
______ ______ _________ _____ _____ _______ ____ ________ ________.
_____ _________ ______ ________ _______ ______ _________ __________ _____ ________ ____.
___ ___ ________ _________ ____ _______ ______.
______ __________ ______ ________ _________ ____.
_____ __________ ___ _______ ______ __________ ____ __________ ________ ____.
___ __________.
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Determine the smallest roots of the following equation:
to three significant digits using
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where
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Perform four iterations (rounded to four decimal places) using
(i) Jacobi Method and
(ii) Gauss-Seidel method,
for the following system of equations
. The exact solution is (1, 2, 3)T. Which method gives better approximation to the exact solution?
For the following data develop difference table and find forward differences and backward differences
| I | xi | yi |
| 0 | -1 | 16.8575 |
| 1 | 0 | 24.0625 |
| 2 | 1 | 16.5650 |
| 3 | 2 | -13.9375 |
| 4 | 3 | 28.5625 |
| 5 | 4 | 144.0625 |