Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.
In Computer Oriented Numerical Techniques Lab, Gauss Elimination method is one of the most widely used techniques for solving a system of linear equations of the form Ax = b, where A is a coefficient matrix, x is the vector of unknowns, and b is the constant vector. The method works in two phases: the forward elimination phase and the back substitution phase. In forward ______ _______ _________ __________ _________ ______ _________ __________ ________ ________ _____ ________.
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Write a program in C to solve the equation from
to
by using Taylor series method of O(h2) with
and
and find the actual error at
if the exact solution is
.
. Write a program in C to find the approximate value of the following definite integral using Trapezoidal rule and obtain a bound for the error. The exact value of correct to six decimal places:
$$
I = \int_0^1 \frac{dx}{1+x}
Write a C Program for solving the following system of equations using Jacobi method:
$$
\begin{bmatrix}
5 & -1 & -1 & -1 \\
-1 & 10 & -1 & -1 \\
-1 & -1 & 10 & -1 \\
-1 & -1 & -1 & 5
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4
\end{bmatrix}
=
\begin{bmatrix}
-4 \\
12 \\
8 \\
34
\end{bmatrix}
Starting with x(0) = (0, 0, 0, 0). The exact solution is x = (1, 2,
Write a program in C for the demonstration of Stirling's Formula for Interpolation.
Write a C Program for solving the following system of equations using Jacobi method:
$$
\begin{bmatrix}
5 & -1 & -1 & -1 \\
-1 & 10 & -1 & -1 \\
-1 & -1 & 10 & -1 \\
-1 & -1 & -1 & 5
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4
\end{bmatrix}
=
\begin{bmatrix}
-4 \\
12 \\
8 \\
34
\end{bmatrix}
Starting with x(0) = (0, 0, 0, 0). The exact solution is x = (1, 2,
Write a program in C that accepts a decimal number and displays its floating-point equivalent number. You may make assumptions to simplify the program, however, your representation of floating point number should be closer to IEEE 754 standard 32 bit representation.
Write a program to implement Gauss Elimination method for solving linear equations. Your method should check if a given pivot is zero or not. It should also minimise the floating-point errors.