{"id":14980919,"url":"https://github.com/iydon/numericalanalysisnotes","last_synced_at":"2025-10-13T11:41:11.335Z","repository":{"id":48833577,"uuid":"147360405","full_name":"iydon/NumericalAnalysisNotes","owner":"iydon","description":"Numerical Analysis Notes and Codes.","archived":false,"fork":false,"pushed_at":"2021-07-09T11:23:13.000Z","size":2939,"stargazers_count":6,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-04-09T03:35:05.255Z","etag":null,"topics":["latex-document","numerical-analysis","sustex"],"latest_commit_sha":null,"homepage":null,"language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/iydon.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2018-09-04T14:36:41.000Z","updated_at":"2023-03-23T22:40:39.000Z","dependencies_parsed_at":"2022-09-23T22:41:43.475Z","dependency_job_id":null,"html_url":"https://github.com/iydon/NumericalAnalysisNotes","commit_stats":null,"previous_names":[],"tags_count":1,"template":false,"template_full_name":null,"purl":"pkg:github/iydon/NumericalAnalysisNotes","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/iydon%2FNumericalAnalysisNotes","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/iydon%2FNumericalAnalysisNotes/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/iydon%2FNumericalAnalysisNotes/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/iydon%2FNumericalAnalysisNotes/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/iydon","download_url":"https://codeload.github.com/iydon/NumericalAnalysisNotes/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/iydon%2FNumericalAnalysisNotes/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":279014804,"owners_count":26085594,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-10-13T02:00:06.723Z","response_time":61,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["latex-document","numerical-analysis","sustex"],"created_at":"2024-09-24T14:02:35.836Z","updated_at":"2025-10-13T11:41:11.316Z","avatar_url":"https://github.com/iydon.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Numerical_Analysis_Notes\n![Windows](https://img.shields.io/badge/platform-Windows-green.svg)\n![TeX](https://img.shields.io/badge/language-TeX-orange.svg)\n![MIT](https://img.shields.io/badge/license-MIT-blue.svg)\n\nNumerical Analysis Notes and Codes. XeLaTeX to compile. (option: '-shell-escape')\n\n# Chapter 1: Mathematical Preliminaries and Error Analysis\n- [ ] 1.1: Review of Calculus\n- [x] 1.2: Round-off Errors and Computer Arithmetic\n- [x] 1.3: Algorithms and Convergence\n- [ ] 1.4: Numerical Software\n\n# Chapter 2: Solutions of Equations in One Variable\n- [x] 2.1 The Bisection Method\n- [x] 2.2 Fixed-Point Iteration\n- [x] 2.3 Newton's Method and Its Extensions\n- [x] 2.4 Error Analysis for Iterative Methods\n- [ ] 2.5 Accelerating Convergence\n- [ ] 2.6 Zeros of Polynomials and Müller's Method\n- [ ] 2.7 Survey of Methods and Software\n\n# Chapter 3: Interpolation and Polynomial Approximation\n- [x] 3.1 Interpolation and the Lagrange Polynomial\n- [x] 3.2 Data Approximation and Neville's Method\n- [x] 3.3 Divided Differences\n- [x] 3.4 Hermite Interpolation\n- [x] 3.5 Cubic Spline Interpolation\n- [ ] 3.6 Parametric Curves\n- [ ] 3.7 Survey of Methods and Software\n\n# Chapter 4: Numerical Differentiation and Integration\n- [x] 4.1 Numerical Differentiation\n- [x] 4.2 Richardson's Extrapolation\n- [x] 4.3 Elements of Numerical Integration\n- [x] 4.4 Composite Numerical Integration\n- [x] 4.5 Romberg Integration\n- [ ] 4.6 Adaptive Quadrature Methods\n- [x] 4.7 Gaussian Quadrature\n- [ ] 4.8 Multiple Integrals\n- [ ] 4.9 Improper Integrals\n- [ ] 4.10 Survey of Methods and Software\n\n# Chapter 5: Initial-Value Problems for Ordinary Differential Equations\n- [x] 5.1 The Elementary Theory of Initial-Value Problems\n- [x] 5.2 Euler’s Method\n- [x] 5.3 Higher-Order Taylor Methods\n- [x] 5.4 Runge-Kutta Methods\n- [x] 5.5 Error Control and the Runge-Kutta-Fehlberg Method\n- [x] 5.6 Multistep Methods\n- [ ] 5.7 Variable Step-Size Multistep Methods\n- [ ] 5.8 Extrapolation Methods\n- [ ] 5.9 Higher-Order Equations and Systems of Differential Equations\n- [ ] 5.10 Stability\n- [ ] 5.11 Stiff Differential Equations\n- [ ] 5.12 Survey of Methods and Software\n\n# Chapter 6: Direct Methods for Solving Linear Systems\n- [x] 6.1 Linear Systems of Equations\n- [x] 6.2 Pivoting Strategies\n- [ ] 6.3 Linear Algebra and Matrix Inversion\n- [ ] 6.4 The Determinant of a Matrix\n- [x] 6.5 Matrix Factorization\n- [ ] 6.6 Special Types of Matrices\n- [ ] 6.7 Survey of Methods and Software\n\n# Chapter 7: IterativeTechniques in Matrix Algebra\n- [x] 7.1 Norms of Vectors and Matrices\n- [x] 7.2 Eigenvalues and Eigenvectors\n- [x] 7.3 The Jacobi and Gauss-Siedel Iterative Techniques\n- [ ] 7.4 Relaxation Techniques for Solving Linear Systems\n- [x] 7.5 Error Bounds and Iterative Refinement\n- [ ] 7.6 The Conjugate Gradient Method\n- [ ] 7.7 Survey of Methods and Software\n\n# Chapter 8: ApproximationTheory\n- [ ] 8.1 Discrete Least Squares Approximation\n- [ ] 8.2 Orthogonal Polynomials and Least Squares Approximation\n- [ ] 8.3 Chebyshev Polynomials and Economization of Power Series\n- [ ] 8.4 Rational Function Approximation\n- [ ] 8.5 Trigonometric Polynomial Approximation\n- [ ] 8.6 Fast Fourier Transforms\n- [ ] 8.7 Survey of Methods and Software\n\n# Chapter 9: Approximating Eigenvalues\n- [ ] 9.1 Linear Algebra and Eigenvalues\n- [ ] 9.2 Orthogonal Matrices and Similarity Transformations\n- [ ] 9.3 The Power Method\n- [ ] 9.4 Householder’s Method\n- [ ] 9.5 The QR Algorithm\n- [ ] 9.6 Singular Value Decomposition\n- [ ] 9.7 Survey of Methods and Software\n\n# Chapter 10: Numerical Solutions of Nonlinear Systems of Equations\n- [ ] 10.1 Fixed Points for Functions of Several Variables\n- [ ] 10.2 Newton’s Method\n- [ ] 10.3 Quasi-Newton Methods\n- [ ] 10.4 Steepest Descent Techniques\n- [ ] 10.5 Homotopy and Continuation Methods\n- [ ] 10.6 Survey of Methods and Software\n\n# Chapter 11: Boundary-Value Problems for Ordinary Differential Equations\n- [ ] 11.1 The Linear Shooting Method\n- [ ] 11.2 The Shooting Method for Nonlinear Problems\n- [ ] 11.3 Finite-Difference Methods for Linear Problems\n- [ ] 11.4 Finite-Difference Methods for Nonlinear Problems\n- [ ] 11.5 The Rayleigh-Ritz Method\n- [ ] 11.6 Survey of Methods and Software\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiydon%2Fnumericalanalysisnotes","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fiydon%2Fnumericalanalysisnotes","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiydon%2Fnumericalanalysisnotes/lists"}