Reward Systems - Money and More
2024-04-11
What is Money ? An oversimplified view of the economic system goes like the following: When Fed increases the money supply, it means banks can now lend more money so loans are provided at a lower rate of interest to companies and people.…
Discrete Vs Continuous
2022-01-26
Introduction In this post, we delve into the mental model (or abstract feeling) of things being continuous Vs discrete. In the direction of continuous vs discrete ideas, we look into signal processing, numerical methods and random ideas.…
Computational Geometry
2020-10-01
Key Resources Textbook: Computational Geometry - Algorithms and Applications Coursera Course: For the Problemset and Implementations (Till Part 5) Philipp Kindermann’s Lectures Series (Part 6 and Onwards) Various Random Resources found on the internet!…
Numerical Analysis
2020-01-20
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.…
Math Modelling
2019-05-20
Important Topics Routh Hurwitz Test Matrix of Variation/Jacobian of dx/dt (and dy/dt) Stability of solution Local Stability (Matrix of Variation) Eigenvalues Positive Definate : Unstable Negative Definate : Local AS Imaginary Eigenvalues: Spiral Global Stability (Appropriate Lyaponov Function) Test stability by Lyapunov Funcn or any other (V) has derivative negative definate $$V(x) = x - x^* - x^* ln(\frac{x}{x^*}) \frac{k_1}{2}(T- T^*)^2 + \frac{k_2}{2}(U-U^*)^2$$…