Bibliografie#
Acest capitol va menționa toate resursele utilizate pe parcursul cărții. Multe dintre acestea au linkuri atașate pentru a fi ușor accesibile celor interesați.
TODO: Suplimentar, adresele conțin în general informații despre ultima accesare.
Bibliografie#
[1]
- A Geometrical Root Finding Method for Polynomials, with Complexity Analysis, 2013, https://arxiv.org/pdf/1308.4217.pdf
[2]
- Orthogonal polynomials: applications and computation, 1996, https://www.cs.purdue.edu/homes/wxg/selected_works/section_04/146.pdf
[3]
- Appendix E (Linear Algebra: Eigenproblems) in Intoduction to Finite Element Methods, 2004, https://quickfem.com/wp-content/uploads/IFEM.AppE_.pdf
[4]
- Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 1964-1970
[5]
[6]
- Automatic Differentiation Step by Step, 2019, https://marksaroufim.medium.com/automatic-differentiation-step-by-step-24240f97a6e6
[7]
- Numerical analysis (9th edition), 2011
[8]
- A First Course in the Numerical Analysis of Differential Equations, 1996
[9]
- Secant Method | Lecture 15 | Numerical Methods for Engineers, 2021, https://www.youtube.com/watch?v=Zz8AYQ8c5-U
[10]
[11]
- Computing and estimating the rate of convergence, 2020, https://www.math-cs.gordon.edu/courses/ma342/handouts/rate.pdf
[12]
- Line search methods, 2021, https://optimization.cbe.cornell.edu/index.php?title=Line_search_methods
[13]
- Cubic Spline Interpolation by Solving a Recurrence Equation Instead of a Tridiagonal Matrix, 2014, https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1314&context=cseconfwork
[14]
- Cubic Splines, https://people.clas.ufl.edu/kees/files/CubicSplines.pdf
[15]
- Economics Professor Wears Funny T-Shirt That Baffles His PhD Students, 2017, https://mymodernmet.com/professors-funny-t-shirt/
[16]
- Metode numerice, în Notițe de laborator
[17]
Singular Value Decomposition (SVD), 2023, https://www.geeksforgeeks.org/singular-value-decomposition-svd/
[18]
- An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, 1994, https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf
[19]
- Richardson's Extrapolation, 2008, https://sites.math.washington.edu/~greenbau/Math_498/lecture04_richardson.pdf
[20]
- Householder Deflation, 1993-2001, https://www.cfm.brown.edu/faculty/gk/AM117/Reading/Deflation/index.html
[21]
Taylor's Series method, https://math.iitm.ac.in/public_html/sryedida/caimna/ode/taylorseries/taylor.html
[22]
[23]
[24]
- The QR Factorization (Numerical analysis MAT 610), 2009-2010, https://www.math.usm.edu/lambers/mat610/sum10/lecture9.pdf
[25]
[26]
[27]
- Matrix decomposition and its modern applications. A rigorous first course, 2022, https://arxiv.org/abs/2107.02579
[28]
- Linear Algebra and Its Applications (4th edition), 2006
[29]
- Gram-Schmidt vs. Modified Gram-Schmidt, 2020-2021, https://laurenthoeltgen.name/post/gram-schmidt/
[30]
- MuPAD Tutorial II / LU, https://www.cfm.brown.edu/people/dobrush/am34/MuPad/LU.html
[31]
- Numerical Solution of Linear Eigenvalue Problems, https://www.cs.ubc.ca/~greif/Publications/EVP_survey_final_rev.pdf
[32]
- Lecture 9 (in MA128A), 2017, https://math.berkeley.edu/~mgu/MA128ASpring2017/MA128ALectureWeek9.pdf
[33]
- Chebyshev approximation, 2017, https://fse.studenttheses.ub.rug.nl/15406/1/Marieke_Mudde_2017_EC.pdf
[34]
- Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming, 2010, https://www.neidinger.net/SIAMRev74362.pdf
[35]
- Newton interpolation, 2014, https://www.uio.no/studier/emner/matnat/math/nedlagte-emner/MAT-INF4140/v14/undervisningsmateriale/newton.pdf
[36]
- Polynomial, Lagrange, and Newton Interpolation, 2017, https://orionquest.github.io/Numacom/lectures/interpolation.pdf
[37]
- Accuracy and Stability of Numerical Algorithms, 2002
[38]
- Newton-Cotes formulas for integration, 2017-2021, https://www.ndsu.edu/pubweb/~novozhil/Teaching/488%20Data/14.pdf
[39]
- Numerical Mathematics (Springer), 2000
[40]
- Orthogonal Functions in Systems and Control in Advanced Series in Electrical and Computer Engineering (Vol. 9), 1995
[41]
[42]
- Essentials of Padé Approximants in Academic Press, 1975
[43]
[44]
- Parallel Scientific Computing in C++ and MPI, 2003
[45]
- Riemann Sums, https://www.math.drexel.edu/~tolya/notes_riemann_sums.pdf
[46]
- Taylor Polynomials of Functions of Two Variables, 2020, https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Multivariable_Calculus/3%3A_Topics_in_Partial_Derivatives/Taylor__Polynomials_of_Functions_of_Two_Variables
[47]
- Calculul valorilor proprii și vectorilor proprii pentru matrice nesimetrice, 2010
[48]
- Calculul iterativ al unui vector propriu. Metoda puterii. Metoda puterii inverse, 2010
[49]
- Algoritmul QR cu deplasare explicită, 2010
[50]
- Understanding Singular Value Decomposition and its Application in Data Science, 2020, https://towardsdatascience.com/understanding-singular-value-decomposition-and-its-application-in-data-science-388a54be95d
[51]
- Formulas for the error in Simpson's rule (in The American Mathematical Monthly, 33(2):76-83), 1926
[52]
- Iterative methods for solving partial difference equations of elliptic type, 1954, https://www.ams.org/journals/tran/1954-076-01/S0002-9947-1954-0059635-7/S0002-9947-1954-0059635-7.pdf
[53]
[54]
- What is the remainder for a taylor series of two variables., 2017, https://math.stackexchange.com/questions/2439286/what-is-the-remainder-for-a-taylor-series-of-two-variables
[55]
Taylor expansion methods for solving ODEs, https://www.colorado.edu/amath/sites/default/files/attached-files/taylor_method_odes.pdf
[56]
- Gauss Jordan Elimination & Reduced Row Echelon Form, 2018, https://www.youtube.com/watch?v=eYSASx8_nyg
[57]
- The modified Gram-Schmidt procedure, https://www.math.uci.edu/~ttrogdon/105A/html/Lecture23.html
[58]
- Successive Over-Relaxation (SOR), 2022, volume Advanced Linear Algebra: Foundations to Frontiers, https://www.cs.utexas.edu/users/flame/laff/alaff/chapter07-sor.html
[59]
[60]
Wikipedia - Bézier curve (Higher-order curves), 2023, https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Higher-order_curves
[61]
Lagrange Interpolating Polynomial, https://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
[62]
Newton-Cotes Formulas (in Wolfram MathWorld), https://mathworld.wolfram.com/Newton-CotesFormulas.html
[63]
- Adaptive Quadrature Method, 2015, https://www3.nd.edu/~zxu2/acms40390F11/sec4-6-adaptive-quadrature.pdf
Licență#
The book "Metode Numerice", written by Valentin-Ioan Vintilă, is licensed under CC BY-NC-SA 4.0 
