The directories here correspond to the four different Assignments of the course of COL726: Numerical Algorithms (Spring 2021) at IIT Delhi. A brief description of these Assignments corresponding to the different topics involved in them is given below:
- A1: Consists of theoretical questions regarding the topics of floating point arithmetic, backward and forward stability, and matrix norms. Analysed different ways of solving a recurrence relation and performed a stability of those methods of obtaining a solution.
- A2: Consists of theoretical questions from the topics of Projectors, SVD, QR-factorization, Gram-Schmidt algorithm, and least-squares regression. Implemented the Modified GS algorithm to get the matrix for orthogonal polynomials and confirmed that with the Legendre polynomials.
- A3: LU and cholesky decomposition were considered here. Along with them, problems based on Iterative methods, Arnoldi, GMRES, and Conjugate gradient method can be found. Also considered different pivoting based aspects to compute the LU decomposition of a matrix and performed a stablity analysis of these methods.
- A4: Various Eigen-value algorithms corresponding to QR-factorization, Hessenberg matrix etc. were considered. Carried out an Analysis of Broyden's method and implemented Netwon's method to find the roots of polynomials and considered the convergence analysis of it.