Everything about QR algorithm

🧭 Start here: a 6-step reading path

1. Read the overview: QR algorithmA 5-minute orientation
2. Skim a recent paper: A Review of Yolo Algorithm DevelopmentsInfluential work since 2022
3. Pick up a classic book: Convergence of the QR algorithmThe most-reprinted book on the subject
4. Read the landmark paper: A fast and elitist multiobjective genetic algorithm: NSGA-IICited 45,300 times
5. Go sideways: Inverse iterationA closely related topic
6. Go sideways: Eigenvalue algorithmA closely related topic

🏆 Landmark papers (most cited)

• A fast and elitist multiobjective genetic algorithm: NSGA-II

  K. Deb, A. Pratap, S. Agarwal · 2002 · IEEE Transactions on Evolutionary Computation · 45,300 citations

• Maximum Likelihood from Incomplete Data Via the EM Algorithm

  A. P. Dempster, N. M. Laird, D. B. Rubin · 1977 · Journal of the Royal Statistical Society Series B: Statistical Methodology · 34,503 citations

• IQ-TREE: A Fast and Effective Stochastic Algorithm for Estimating Maximum-Likelihood Phylogenies

  Lam-Tung Nguyen, Heiko A. Schmidt, Arndt von Haeseler · 2014 · Molecular Biology and Evolution · 25,788 citations

• SPAdes: A New Genome Assembly Algorithm and Its Applications to Single-Cell Sequencing

  Anton Bankevich, Sergey Nurk, Dmitry Antipov · 2012 · Journal of Computational Biology · 25,686 citations

• An Algorithm for Least-Squares Estimation of Nonlinear Parameters

  Donald W. Marquardt · 1963 · Journal of the Society for Industrial and Applied Mathematics · 25,468 citations

• A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood

  Stéphane Guindon, Olivier Gascuel · 2003 · Systematic Biology · 14,682 citations

• The Whale Optimization Algorithm

  Seyedali Mirjalili, Andrew Lewis · 2016 · Advances in Engineering Software · 14,187 citations

• A Fast Learning Algorithm for Deep Belief Nets

  Geoffrey E. Hinton, Simon Osindero, Yee-Whye Teh · 2006 · Neural Computation · 13,406 citations

🆕 Influential since 2022

• A Review of Yolo Algorithm Developments

  Peiyuan Jiang, Daji Ergu, Fangyao Liu · 2022 · Procedia Computer Science · 2,698 citations

• Particle Swarm Optimization Algorithm and Its Applications: A Systematic Review

  Ahmed G. Gad · 2022 · Archives of Computational Methods in Engineering · 1,869 citations

• Dung beetle optimizer: a new meta-heuristic algorithm for global optimization

  Jiankai Xue, Bo Shen · 2022 · The Journal of Supercomputing · 1,759 citations

• Reptile Search Algorithm (RSA): A nature-inspired meta-heuristic optimizer

  Laith Abualigah, Mohamed Abd Elaziz, Putra Sumari · 2022 · Expert Systems with Applications · 1,394 citations

• Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems

  Fatma A. Hashim, Essam H. Houssein, Kashif Hussain · 2022 · Mathematics and Computers in Simulation · 1,301 citations

📚 Books worth reading

• Convergence of the QR algorithmBeresford Parlett · 1964
• Pervasive Computing and the Networked WorldQiaohong Zu · 2013
• 📕The minimal residual QR-factorization algorithm for reliably solving subset regression problemsM. H. Verhaegen · 1987
• A parallel algorithm synthesis procedure for high-performance computer architecturesIan N. Dunn, Gerard G.L. Meyer · 2003
• Adaptive and Natural Computing AlgorithmsMarco Tomassini · 2013
• Total least squares and errors-in-variables modelingSabine van Huffel · 2002
• High Performance Computing for Computational Science - VECPAR 2012Michel Daydé · 2013
• Coding the MatrixPhilip N. Klein · 2013

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Inverse iteration In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate…
• Eigenvalue algorithm In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue…
• Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by ⁠A=QDQ−𝟣⁠…
• Bidiagonal matrix In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below…
• Singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed…
• Arnoldi iteration In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation…
• QR decomposition In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of…
• Numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which…