Everything about Jacobi method

🧭 Start here: a 6-step reading path

1. Read the overview: Jacobi methodA 5-minute orientation
2. Skim a recent paper: Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equationsInfluential work since 2022
3. Pick up a classic book: Variational Principles in PhysicsThe most-reprinted book on the subject
4. Read the landmark paper: Perron’s method for Hamilton-Jacobi equationsCited 280 times
5. Go sideways: Successive over-relaxationA closely related topic
6. Go sideways: Matrix splittingA closely related topic

🏆 Landmark papers (most cited)

• Perron’s method for Hamilton-Jacobi equations

  Hitoshi Ishii · 1987 · Duke Mathematical Journal · 280 citations

• New generalized Jacobi elliptic function rational expansion method

  Ahmad T. Ali · 2011 · Journal of Computational and Applied Mathematics · 119 citations

• The Jacobi method for real symmetric matrices

  H. Rutishauser · 1966 · Numerische Mathematik · 95 citations

• A Jacobi–Jacobi dual-Petrov–Galerkin method for third- and fifth-order differential equations

  E.H. Doha, A.H. Bhrawy, R.M. Hafez · 2011 · Mathematical and Computer Modelling · 55 citations

• A Jacobi--Davidson Type SVD Method

  Michiel E. Hochstenbach · 2001 · SIAM Journal on Scientific Computing · 52 citations

• The Jacobi Method for Real Symmetric Matrices

  H. H. Goldstine, F. J. Murray, J. von Neumann · 1959 · Journal of the ACM · 52 citations

• The Hamilton-Jacobi method and Hamiltonian maps

  S S Abdullaev · 2002 · Journal of Physics A: Mathematical and General · 38 citations

• Scheduled Relaxation Jacobi method: Improvements and applications

  J.E. Adsuara, I. Cordero-Carrión, P. Cerdá-Durán · 2016 · Journal of Computational Physics · 37 citations

🆕 Influential since 2022

• Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations

  Mahmoud A. Zaky, Ahmed S. Hendy, D. Suragan · 2022 · Applied Numerical Mathematics · 26 citations

• Jacobi method for dual quaternion Hermitian eigenvalue problems and applications

  Wenxv Ding, Ying Li, Musheng Wei · 2024 · Journal of Applied Mathematics and Computing · 12 citations

• The Carleman convexification method for Hamilton-Jacobi equations

  Huynh P.N. Le, Thuy T. Le, Loc H. Nguyen · 2024 · Computers & Mathematics with Applications · 9 citations

• Jacobi‐Galerkin Spectral Method for the Fractional Diffusion Equation

  Lizhen Chen, Wenfei Lv, Jing Zhang · 2026 · Numerical Methods for Partial Differential Equations · 4 citations

• Vectorization of a Thread-Parallel Jacobi Singular Value Decomposition Method

  Vedran Novaković · 2023 · SIAM Journal on Scientific Computing · 4 citations

📚 Books worth reading

• Variational Principles in PhysicsJean-Louis Basdevant · 2006
• 📕Tensor-GMRES method for large sparse systems of nonlinear equationsDan Feng · 1994
• 📕Flux Jacobian matrices and generalized Roe average for an equilibrium real gasMarcel Vinokur · 1988
• Surface evolution equationsYoshikazu Giga · 2006
• 📕On the quadratic convergence of a generalization of the Jacobi method to arbitrary matricesAxel H. Ruhe · 1967
• 📕Prediktor-Korrektor-Methoden mit variablen KoeffizientenSándor Frivaldsky · 1983
• 📕A discontinuous Galerkin finite element method for Hamilton-Jacobi equationsChang-Qing Hu · 1998
• 📕An extension of elementary symmetric polynomials and power sums to the case of multivariate polynomialsUlrike Maier · 2001

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

🔗 Related topics

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