Readme.md

System of Linear Equations and Eigen Value Problems

Module 2

We will have to enter the adjacency or the Coefficient matrix into A, which we obtain by extracting the coefficients from the system of linear equations.
We will have to ensure that this matrix A is diagonally dominant, which is a condition for this method to function properly.
We also feed in the RHS values into b.
We also need to key in the initial solution that we can decide upon based on the question in hand.
We should also enter the accuracy_decimal, which is the decimal place accuracy to which answer should be obtained, the number of iterations taken by the code depends on this value.
To prevent the non-convergence condition, the code will proceed till a maximum of 20 iterations is reached.
The code prints the estimated value at the end of every iteration along with the error which is also essential in this method.

We will have to perform an LU Decomposition of the coefficient matrix A and feed them into L and U for the Lower and the Upper diagonal Matrices respectively.
Though this process can be automated by the lu() function, the results obtained here does not match with the ones obtained by the method followed by us currrently. Using that too should yield you the same end result, but I am currently also focussed more on the output of each step than the final result.
We will have to ensure that all the leading sub-matrices of the matrix A has a non-zero determinant.
We also feed in the RHS values into b.
The code prints the L inverse, Z where Z=L_inv*b, U inverse, and the final result X.

We will have to enter the adjacency or the Coefficient matrix into A, which we obtain by extracting the coefficients from the system of linear equations.
We have to ensure that A is a tri-diagonal system.
We also feed in the RHS values into b.
The code prints the d-- diagonal elements, a -- upper diagonal elements, b -- lower diagonal elements, r -- rhs or residue values, the a, and r values during the Forward elimination step, the x values during the Backward Substitution step, and the final X values which is the solution to the system of equations.

We will have to enter the matrix into A.
We also need to key in the initial solution into X_cur that we can decide upon based on the question in hand.
We should also enter the accuracy_decimal, which is the decimal place accuracy to which answer should be obtained, the number of iterations taken by the code depends on this value.
To prevent the non-convergence condition, the code will proceed till a maximum of 20 iterations is reached.
The code displays the P, X, and the normalzing value which is the maximum value among the P values, all for every iteration.
The final X_cur displayed is the dominant eigen value of the entered matrix

Coming Soon