Numericalmethods

Dive into the abstract feelings of things being continuous and discrete, with various examples.

Resources Jacob Bishop’s Tutorials Part 5-7 covers most topics Gauss Quadrature Vs Newton Cotes’ Visualization Check Calculator function input for Iterative Approximation Methods( Newton-Rhapson, Fixed Point Iteration etc.) Basic Analysis Catastrophic Cancellation Significant Digits Vs Decimal points Sum for minimal error, rounding/chopping Taylor Series’ Approximation and Error Iterative Methods Bisection Regula Falsi (Method of Chords) Secant Swap to whichever is close Fixed Point Iteration Order of convergences Uniqueness Error Analysis Newton Raphson Order of convergences Matrix Techniques Pivoting (Partial Pivoting = Every Step) Scaling First before Pivoting Matrix Norms Norm_1(A) = max(col sum) Norm_inf(A) = max(row sum) Norm_2(A) = Spectral Norm = $\sqrt \lambda$ for eigenvalue Norm_F(A) = root of(Sum of all a_ij^2) = Frobenius Norm Conditional No. = ||A|| * ||A^-1|| Matrix Iterative Methods In order to solve, systems of equation we have Gauss-El-M, Gauss-Jacobi and Gauss-Siedel. Jacobi and Siedel is mostly used for sparse arrays where G-El-M is highly ineffecient. Newton-Raphson, Fixed Point are iterative methods also work while finding solution. ...