Numerical Methods
Following are the lecture notes and topics covered for Numerical Methods course.
| 1/Sep-20/Sep,2016 |
# Floating Point Arithmetics
# Gaussian Elimination
# LU Factorization
# Condition Number of Matrices
# Cholesky Method
# Symmetric Positive Definite Matrices
# Linear Least Squares
# Orthogonal Matrices
# QR factorization
# Gaussian Elimination
# LU Factorization
# Condition Number of Matrices
# Cholesky Method
# Symmetric Positive Definite Matrices
# Linear Least Squares
# Orthogonal Matrices
# QR factorization
| 20/Sep-18/Oct,2016 |
# Singular Value Decomposition
# SVD & Least Squares Problem
# Eigenvalues
# Gershgorin Theorem
# Eigenvalue Decomposition
# Shifted Inverse Iterations
# Convergence Rate
# Fixed Point Iteration
# Newton's Method
# Secant Method
# System of Non-Linear equations
# SVD & Least Squares Problem
# Eigenvalues
# Gershgorin Theorem
# Eigenvalue Decomposition
# Shifted Inverse Iterations
# Convergence Rate
# Fixed Point Iteration
# Newton's Method
# Secant Method
# System of Non-Linear equations
| 27/Oct-1/Nov,2016 |
# Constrained Optimization
# Convexity
# Optimality Condidtions
# Stationary Points
# Necessary/Sufficient Conditions for Constrained Optimization
# Linear Programming
# Convexity
# Optimality Condidtions
# Stationary Points
# Necessary/Sufficient Conditions for Constrained Optimization
# Linear Programming
| 3/Nov-15/Nov,2016 |
# Unconstrained Minimization
# Non-Linear Least Squares
# Quadratic Programming
# Lagrange Interpolation
# Newton Interpolation
# Hermite Interpolation
# Non-Linear Least Squares
# Quadratic Programming
# Lagrange Interpolation
# Newton Interpolation
# Hermite Interpolation
| 17/Nov-24/Nov,2016 |
# Piecewise Cubic Interpolation
# Numerical Integration
# Polynomial Integration
# Romberg Intergration
# Legendre Polynomials
# Chebyshev Polynomials
# Gaussian Quadrature
# Numerical Differentiation
# Systems of First-Order ODEs
# Forward/Backward Euler
# Numerical Integration
# Polynomial Integration
# Romberg Intergration
# Legendre Polynomials
# Chebyshev Polynomials
# Gaussian Quadrature
# Numerical Differentiation
# Systems of First-Order ODEs
# Forward/Backward Euler
| 29/Nov-15/Dec,2016 |
# Stability Region
# Multistep Methods
# Adams-Moulton Method
# Stiff ODEs
# BDF Method
# Finite Differences for BVP
# Galekin Method
# Multistep Methods
# Adams-Moulton Method
# Stiff ODEs
# BDF Method
# Finite Differences for BVP
# Galekin Method
