Compute the value of the integral
by using
Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule
The integral to evaluate is: $$ \int_{8.4}^{10.4} (5x + 4x^2 + 3) \, dx $$ Let us solve it numerically using $n = 4$ subintervals for clarity. The width of each subinterval is: $$ h = \frac{10.4 - 8.4}{4} = \frac{2}{4} = 0.5 $$ The points are: $x_0 = 8.4, x_1 = __________ ______ __________ ______ _____ ___ _______ ________ ___ _______ ____ __________.
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Solve the system of equations
using Gauss elimination method with partial pivoting.
If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
Explain what is the role of interpolation in solving numerical problems?
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 |
Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method
Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow
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?