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Lecture 31 of 63week-06

Week 6 : Lecture 31 : Nonlinear Equations: Convergence Theorem of Secant Method

Prof. S. Baskar · IIT Bombay

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Numerical Analysis, IIT Bombay (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

  1. Week 1 : Lecture 1 : Introduction Video
  2. Week 1 : Lecture 2 : Mathematical Preliminaries: Taylor Approximation Video
  3. Week 1 : Lecture 3 : Mathematical Preliminaries: Order of Convergence Video
  4. Week 1 : Lecture 4 : Arithmetic Error: Floating-point Approximation Video
  5. Week 1 : Lecture 5 : Arithmetic Error: Significant Digits Video
  6. Week 1 : Lecture 6 : Arithmetic Error: Condition Number and Stable Computation Video
  7. Week 2 : Lecture 7 : Tutorial Session - 1: Problem Solving Video
  8. Week 2 : Lecture 8 : Python Coding: Introduction Video
  9. Week 2 : Lecture 9 : Linear Systems: Gaussian Elimination Method Video
  10. Week 2 : Lecture 10 : Linear Systems: LU-Factorization (Doolittle and Crout) Video
  11. Week 2 : Lecture 11 : Linear Systems: LU-Factorization (Cholesky) Video
  12. Week 3 : Lecture 12 : Linear Systems: Operation Count for Direct Methods Video
  13. Week 3 : Lecture 13 : Tutorial Session - 2: Python Coding for Naive Gaussian Elimination Method Video
  14. Week 3 : Lecture 14 : Tutorial Session - 3: Python Coding for Thomas Algorithm Video
  15. Week 3 : Lecture 15 : Matrix Norms: Subordinate Matrix Norms Video
  16. Week 3 : Lecture 16 : Matrix Norms: Condition Number of a Matrix Video
  17. Week 4 : Lecture 17 : Iterative Methods: Jacobi Method Video
  18. Week 4 : Lecture 18 : Iterative Methods: Convergence of Jacobi Method Video
  19. Week 4 : Lecture 19 : Iterative Methods: Gauss-Seidel Method Video
  20. Week 4 : Lecture 20 : Iterative Methods: Convergence Analysis of Iterative Methods Video
  21. Week 4 : Lecture 21 : Iterative Methods: Successive Over Relaxation Method Video
  22. Week 5 : Lecture 22 : Tutorial Session - 4: Python implementation of Jacobi Method Video
  23. Week 5 : Lecture 23 : Eigenvalues and Eigenvectors: Power Method (Construction) Video
  24. Week 5 : Lecture 24 : Eigenvalues and Eigenvectors: Power Method (Convergence Theorem) Video
  25. Week 5 : Lecture 25 : Eigenvalues and Eigenvectors: Gerschgorin's Theorem and Applications Video
  26. Week 5 : Lecture 26 : Eigenvalues and Eigenvectors: Power Method (Inverse and Shifted Methods) Video
  27. Week 6 : Lecture 27 : Nonlinear Equations: Overview Video
  28. Week 6 : Lecture 28 : Nonlinear Equations: Bisection Method Video
  29. Week 6 : Lecture 29 : Tutorial Session - 5: Implementation of Bisection Method Video
  30. Week 6 : Lecture 30 : Nonlinear Equations: Regula-falsi and Secant Methods Video
  31. Week 6 : Lecture 31 : Nonlinear Equations: Convergence Theorem of Secant Method Video
  32. Week 7 : Lecture 32 : Nonlinear Equations: Newton-Raphson's method Video
  33. Week 7 : Lecture 33 : Nonlinear Equations: Newton-Raphson's method (Convergence Theorem) Video
  34. Week 7 : Lecture 34 : Nonlinear Equations: Fixed-point Iteration Methods Video
  35. Lecture 35:Nonlinear Equations: Fixed-point Iteration Methods (Convergence)&Modified Newton's Method Video
  36. Week 7 : Lecture 36 : Nonlinear Equations: System of Nonlinear Equations Video
  37. Week 8 : Lecture 37 : Nonlinear Equations: Implementation of Newton-Raphson's Method as Python Code Video
  38. Week 8 : Lecture 38 : Polynomial Interpolation: Existence and Uniqueness Video
  39. Week 8 : Lecture 39 : Polynomial Interpolation: Lagrange and Newton Forms Video
  40. Week 8 : Lecture 40 : Polynomial Interpolation: Newton’s Divided Difference Formula Video
  41. Week 8 : Lecture 41 : Polynomial Interpolation: Mathematical Error in Interpolating Polynomial Video
  42. Week 9 : Lecture 42 : Polynomial Interpolation: Arithmetic Error in Interpolating Polynomials Video
  43. Week 9 : Lecture 43 : Polynomial Interpolation: Implementation of Lagrange Form as Python Code Video
  44. Week 9 : Lecture 44: Polynomial Interpolation: Runge Phenomenon & Piecewise Polynomial Interpolation Video
  45. Week 9 : Lecture 45 : Polynomial Interpolation: Hermite Interpolation Video
  46. Week 9 : Lecture 46 : Polynomial Interpolation: Cubic Spline Interpolation Video
  47. Week 10 : Lecture 47 : Polynomial Interpolation: Tutorial Session Video
  48. Week 10 : Lecture 48 : Numerical Integration: Rectangle Rule Video
  49. Week 10 : Lecture 49 : Numerical Integration: Trapezoidal Rule Video
  50. Lecture 50 : Numerical Integration: Simpson's Rule Video
  51. Week 10 : Lecture 51 : Numerical Integration: Gaussian Quadrature Rule Video
  52. Week 11 : Lecture 52 : Numerical Integration: Tutorial Session Video
  53. Week 11 : Lecture 53 : Numerical Differentiation: Primitive Finite Difference Formulae Video
  54. Lecture 54 : Numerical Differentiation: Method of Undetermined Coefficients and Arithmetic Error Video
  55. Week 11 : Lecture 55 : Numerical ODEs: Euler Methods Video
  56. Week 11 : Lecture 56 : Numerical ODEs: Euler Methods (Error Analysis) Video
  57. Week 12 : Lecture 57 : Numerical ODEs: Runge-Kutta Methods Video
  58. Week 12 : Lecture 58 : Numerical ODEs: Modified Euler's Methods Video
  59. Week 12 : Lecture 59 : Numerical ODEs: Multistep Methods Video
  60. Week 12 : Lecture 60 : Numerical ODEs: Stability Analysis Video
  61. Week 12 : Lecture 61 : Numerical ODEs: Two-point Boundary Value Problems Video
  62. Live Session 21-02-2024 Video
  63. Live Session 06-03-2025 Video