bhanushri123 / NumericalMethods

NumericalMethods

• pivot(row_i, row_j, A): Performs row pivoting on a given matrix A by swapping rows row_i and row_j.

• scale(row_i, λ, A): Scales a specified row row_i of a matrix A by a scalar factor λ.

• Tmatrix(A): Computes the upper triangular matrix using Gaussian elimination on matrix A.

• matmul(A, B): Calculates the number of arithmetic operations required to multiply two matrices A and B.

• checksym(A): Checks if a matrix A is symmetric and returns True if it is.

• cholesky_decomposition(A): Computes the Cholesky decomposition of a matrix A.

• gaus_seidal(A, b, x0, tol, max_iterations): Implements the Gauss-Seidel method to solve a system of linear equations.
  

• jacobi(A, b, x0, tol, max_iterations): Implements the Jacobi method to solve a system of linear equations.

• CycTridJacobi(n, tol, max_iterations): Solves a tridiagonal linear system using the Jacobi iterative method.

• bisection(f, x0, x1, kmax, tol): Implements the bisection method to find the root of a given function f within an interval [x0, x1].

1. pivot - Used for row pivoting in matrix operations.
2. scale - Used for scaling a row in a matrix.
3. Tmatrix - Used for computing the upper triangular matrix using Gaussian elimination.
4. matmul - Used for matrix multiplication and counting arithmetic operations.
5. checksym - Used for checking if a matrix is symmetric.
6. cholesky_decomposition - Used for computing the Cholesky decomposition of a matrix.
7. gaus_seidal - Used for solving a system of linear equations using the Gauss-Seidel method.
8. jacobi - Used for solving a system of linear equations using the Jacobi method.
9. CycTridJacobi - Used for solving a tridiagonal linear system using the Jacobi iterative method.
10. bisection - Used for finding the root of a function within an interval using the bisection method.

These are the method names used throughout code for various mathematical and computational operations.