Learn · Applied Numerical Methods
Lecture 48 of 127Week 5
Lecture 48 - Errors in polynomial interpolations
Prof. Malay K. Das · IIT Kanpur
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All the lectures
- Lecture 01 - Outline
- Lecture 02 - Course Policy
- Lecture 03 - Example
- Lecture 04 - Introduction
- Lecture 05 - Modeling
- Lecture 06 - Validation
- Lecture 07 - Bisection method
- Lecture 08 - Newton Raphson method
- Lecture 09 - Week 1 closure
- Lecture 10 - Outline
- Lecture 11 - Python Fundamentals
- Lecture 12 - Python Fundamentals
- Lecture 13 - Pseudocode
- Lecture 14 - Python Program for gcd
- Lecture 15 - Numpy Fundamentals
- Lecture 16 - Numpy vectorized operations
- Lecture 17 - Numpy Exercise
- Lecture 18 - Python Programming: Closure
- Lecture 19 - Outline
- Lecture 20 - Linear Algebra: Outline
- Lecture 21: Vectors
- Lecture 22: Linear Equations
- Lecture 23: Matrix Algebra
- Lecture 24: Special Matrices
- Lecture 25: Gaussian Elimination
- Lecture 26: Gaussian Elimination: Generalization
- Lecture 27: Gaussian Elimination: Elementary Operations
- Lecture 28: Partial Pivoting
- Lecture 29: Scaling
- Lecture 30 - LU Decomposition
- Lecture 31 - LU Decomposition CROUT/DOOLITTLE Methods
- Lecture 32 - System of Simultaneous Non-Linear Equations
- Lecture 33 - Direct vs Iterative Linear Solvers
- Lecture 34 - Jacobi Iteration
- Lecture 35 - Gauss Seidel Method, Successive Overrelaxation
- Lecture 36 - Iterative Linear Solvers: Theory
- Lecture 37 - Iterative Linear Solvers: Convergence
- Lecture 38 - Eigenvalues and Eigenvectors: Power Method
- Lecture 39 - Inverse Power Method
- Lecture 40 - Power Method: Theory
- Lecture 41 - Closure
- Lecture 42 - Outline
- Lecture 43 - Calculus: Outline
- Lecture 44 - Polynomial Interpolation
- Lecture 45 - Newton's Interpolating Polynomials
- Lecture 46 - Lagrange Interpolating Polynomials
- Lecture 47 - Lagrange Polynomials: Example
- Lecture 48 - Errors in polynomial interpolations
- Lecture 49 - Numerical differentiation: finite difference method
- Lecture 50 - Numerical Differentiation: Truncation Error
- Lecture 51 - Numerical Differentiation: Double Derivative
- Lecture 52 - Higher Order Numerical Differentiation: Finite DIfference Method
- Lecture 53 - Numerical Differentiation: General Procedure
- Lecture 54 - Numerical Differentiation: Nonuniform Grids
- Lecture 55 - Numerical Differentiation: Polynomial Interpolation
- Lecture 56 - Partial Derivatives: Numerical Procedure
- Lecture 57 - Numerical Differentiation: Example
- Lecture 58: Closure
- Lecture 59: Outline
- Lecture 60 - Numerical Integration: Trapezoidal Rule
- Lecture 61 - Simpson's One-Third Rule
- Lecture 62 - Simpson's 3/8 rule
- Lecture 63 - Numerical Integration: Example
- Lecture 64 - Gaussian Quadrature
- Lecture 65 - Double Integral
- Lecture 66 - Closure
- Lecture 67 - Outline
- Lecture 68 - Ordinary Differential Equations (ODE)
- Lecture 69 - First Order ODE
- Lecture 70 - Ordinary Differential Equations: Euler Method
- Lecture 71 - Runge-Kutta Method
- Lecture 72 - Higher-Order IVP
- Lecture 73 - Application: Poplulation Growth Models
- Lecture 74 - Boundary Value Problem: Shooting Method
- Lecture 75 - BVP: Finite Difference Method ((FDM)
- Lecture 76 - FDM: Differential to Difference Equations
- Lecture 77 - Solution of Tridiagonal Systems: Thomas Algorithm
- Lecture 78 - Closure
- Lecture 79 - Outline
- Lecture 80 - Partial Differential Equations (PDE): Introduction
- Lecture 81 - Heat Conduction (Diffusion) Equation
- Lecture 82 - 1D Transient Diffusion: nondimensionalization
- Lecture 83 - 1D Transient Diffusion: Analytical Solution
- Lecture 84 - 1D Transient Diffusion: Explicit Scheme
- Lecture 85 - Numerical Experiments with Explicit Scheme
- Lecture 86 - Stability of Explicit Scheme
- Lecture 87 - 1D Transient Diffusion: Implicit, Crank-Nicolson (CN) Scheme
- Lecture 88 - Stability of Implicit, CN Schemes
- Lecture 89 - Closure
- Lecture 90 - Outline
- Lecture 91 - Heat transfer in a nuclear fuel rod
- Lecture 92 - Discretization of Poisson's equation
- Lecture 93 - Review of Gauss-Seidal Method
- Lecture 94 - Solution of Poisson's equation
- Lecture 95 - Solution of Poisson's equation
- Lecture 96 - Validating our solution
- Lecture 97 - Suggested project: cooling of electronic chip
- Lecture 98 - Discretization: 2D unsteady conduction
- Lecture 99 - Alternating direction implicit (ADI) method
- Lecture 100 - Stability
- Lecture 101 - Closure
- Lecture 102 - Outline
- Lecture 103 - Regression: Learning from data
- Lecture 104 - Simple Linear Regression: Theory
- Lecture 105 - Regression Quality
- Lecture 106 - Simple Linear Regression: Example
- Lecture 107 - Multiple Linear Regression
- Lecture 108 - Linear Regression: vector-matrix notation
- Lecture 109 - Nonlinear Regression: Linearization
- Lecture 110 - Regression: Closure
- Lecture 111 - Outline
- Lecture 112 - Optimization: example, definition
- Lecture 113 - 1D unconstrained optimization: Random search
- Lecture 114 - Golden Section Search
- Lecture 115 - Newton-Raphson Method
- Lecture 116 - Multidimensional unconstrained optimization
- Lecture 117 - Gradients and its significance
- Lecture 118 - Steepest Descent Method
- Lecture 119 - Steepest Descent: Exercise
- Lecture 120 - Newton's Method
- Lecture 121 - Optimization: Closure
- Lecture 122 - Outline
- Lecture 123 - Machine Learning
- Lecture 124 - Artificial Neuron
- Lecture 125 - Artificial Neuron: Perception
- Lecture 126 - Artificial Neural Network
- Lecture 127 - Artificial Neural Network: Closure