numericAnalysis

A repository that implements algorithms in the book "Numerical Analysis", Ninth Edition, by Richard L. Burden and J. Douglas Faires

The progress bar css but unfortunately Github is not allowing the style tag.

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To-Do List:

Next Step: Chapter 5

Chapter 2: Solutions of Equations in One Variable

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• Chapter 2.1 The Bisection Method
• Chapter 2.2 Fixed-Point Iteration
• Chapter 2.3 Newtons's Method and Its Extensions
• Chapter 2.4 Error Analysis for Iterative Methods
  • Modified Newton Method
• Chapter 2.5 Accelerating Convergence
  • Aitken's $\Delta^2$ Method
• Chapter 2.6 Zeros of Polynomials and Muller's Method
  • Horner's method incorperate with Newton's method to find the zeros of polynomial

Chapter 3: Interpolation and Polynomial Approximation

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• Chapter 3.1 Interpolation and the Lagrange Polynomial
• Chapter 3.2 Data Approximation and Neville's Method
• Chapter 3.3 Divided Differences
• Chapter 3.4 Hermite Interpolation
• Chapter 3.5 Cubic Spline Interpolation
• Beyond the Book: -[x] Bezier Curve -[x] Non-Uniform Rational B-Spline

Chapter 4: Numerical Differentiation and Integration

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• Chapter 4.1 Numerical Differentiation
• Chapter 4.2 Richardson's Extrapolation
  • Implement Richardson's Extrapolation algorithm for even order of $h$
• Chapter 4.3 Elements of Numerical Integration
  • Newton-Cotes Formula
• Chapter 4.4 Composite Numerical Integration
  • Visualization
  • General Composite Integral Algorithm
• Chapter 4.5 Romberg Integration
• Chapter 4.6 Adaptive Quadrature Methods
  • Adaptive Trapezoidal rule
  • Adaptive Closed Newton-Cotes
• Chapter 4.7 Gaussian Quadrature
  • Gaussian-Legendre Quadrature
• Chapter 4.8 Multiple Integrals
  • Double and Triple Closed Newton-Cotes

Chapter 5: Initial-Value Problems for ODEs

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• Chapter 5.2 Euler's Method
• Chapter 5.3 Higher-Order Taylor Methods
  • Taylor's method
• Chapter 5.4 Runge-Kutta Methods
  • More in detail about Runge-Kutta Methods
• Chapter 5.5 Error Control and the Runge-Kutta-Fehlberg Method
  • Implement Generalized Runge-Kutta Embedded
• Chapter 5.6 Multistep Method
  • Generalized Adams-Bashforth Algorithm
  • Milne-Simpson Predictor-Corrector
  • Generalized Predictor-Corrector Using Newton-Cotes Formulae
• Chapter 5.7 Variable Step-Size Multistep Method
  • Generalized Variable Step-Size MultiStep Method
• Chapter 5.8 Extrapolation
• Chapter 5.9 Higher-Order Equations and Systems of Differential Equations
• Chapter 5.11 Stiff Differential Equations

Chapter 6: Direct Method for Solving Linear Systems

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• Chapter 6.1 Linear Systems of Equations
• Chapter 6.3 Linear Algebra and Matrix Inversion
  • Algorithm to find the inverse of the matrix
• Chapter 6.4 The Determinant of a Matrix
  • Compute determinant using Gaussian Elimination
• Chapter 6.5 Matrix Factorization
  • PLU Decomposition
• Chapter 6.6 Special Types of Matrices
• PLDL' Decomposition (Refer to the book Matrix Computation)
• Remaining algorithm that solves tridiagonal linear system

Chapter 7: Iterative Techniques in Matrix Algebra

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• Chapter 7.3 The Jacobi and Gauss-Siedel Iterative Techniques
• Chapter 7.4 Relaxation Techniques for Solving Linear Systems
• Chaoter 7.6 The Conjugate Gradient Method
  • Conjugate Gradient Method
  • Biconjugate Gradient Method
  • Biconjuagte Gradient Stabilized Method
  • Conjugate Gradient Squared Method
  • Minimal Residual Method
  • Generalized Minimal Residual Method

Chapter 8: Approximation Theory

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Chapter 9: Approximating Eigenvalues

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Chapter 10: Numerical Solutions of Nonlinear Systems of Equations

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Chapter 11: Boundary-Value Problems for ODE

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Chapter 12: Numerical Solutionns to PDE

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