Homework	Description
HW1	Examination of floating point precision: Analysis of conversion errors in floating point systems, focusing on machine precision impacts and error accumulation during operations. Includes detailed experiments on error translation, addition within the floating point system, and cumulative errors.
HW2	LU Decomposition Techniques: Detailed exploration of LU decomposition, emphasizing the impact of pivot selection, handling of ill-conditioned matrices, and round-off errors during matrix factorization. Various pivoting methods are compared, assessing their effects on solution accuracy and stability.
HW3	Steepest Descent and Conjugate Gradient Methods: Evaluation of iterative methods for solving large linear systems, with a focus on the role and effectiveness of different preconditioners. The study emphasizes preconditioning's impact on convergence rates and the overall performance of the methods.
HW4	Root-Finding Algorithms: Implementation and comparison of bisection, Newton's, and fixed-point methods for finding roots of specific functions. This involves assessing convergence behaviors, the impact of initial values, and exploring the algorithms' performance through empirical tests and visualizations.