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Everything about Convergence problem
In the analytic theory of continued fractions, the convergence problem is the determination of conditions on the partial numerators ai and partial denominators bi that are sufficient to guarantee the convergence of the infinite continued fraction Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Convergence problemA 5-minute orientation
- Skim a recent paper: Linear Regression Problem Relaxations Solved by Nonconvex ADMM With Convergence AnalysisInfluential work since 2022
- Pick up a classic book: On the local convergence of pattern searchThe most-reprinted book on the subject
- Read the landmark paper: Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational InteractionCited 3,495 times
- Go sideways: Solving quadratic equations with continued fractionsA closely related topic
- Go sideways: Periodic continued fractionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction
The convergence problem for differential games
Hilbertian convex feasibility problem: Convergence of projection methods
Uniform convergence of a singular perturbation problem
Local convergence in Fermat's problem
Sensory Convergence Solves a Motion Ambiguity Problem
The split equilibrium problem and its convergence algorithms
Convergence verification of the Collatz problem
🆕 Influential since 2022
Linear Regression Problem Relaxations Solved by Nonconvex ADMM With Convergence Analysis
Convergence rate analysis of Galerkin approximation of inverse potential problem
Fractal basins of convergence in the restricted rhomboidal six-body problem
The Convergence Problem in Mean Field Games with Neumann Boundary Conditions
Indeterminate Stieltjes Moment Problem: Entropy Convergence
📚 Books worth reading
- 📕On the local convergence of pattern searchElizabeth D. Dolan · 2000
- 📕Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatmentDaniele Funaro · 1989
- 📕Approximation of the Newton step by a defect correction processE. Arian · 1999
Differential EquationsMarcelo Viana, Jose Maria Espinar Garcia · 2021
Classical potential theory and its probabilistic counterpartJoseph L. Doob · 1984- 📕Precauchy spacesNandita Rath · 1994
- 📕Integralʹnye uravnenii͡a︡, nekorrektnye zadachi i uluchshenie skhodimostiKrylov, V. I. · 1984
Cours de probabilités et de statistiquesLeboeuf Guegand · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Complete quotient In the metrical theory of regular continued fractions, the kth complete quotient ζ k is obtained by ignoring the first k partial denominators ai. For example…
- Padé table In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants Rm, n to a given complex formal power series…
- Restricted partial quotients In mathematics, and more particularly in the analytic theory of regular continued fractions, an infinite regular continued fraction x is said to be restricted…
- Continued fraction b0+a1b1+a2b2+a3b3+⋱ A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction…
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- Simple continued fraction A simple or regular continued fraction is a continued fraction with numerators all equal to one, and denominators built from a sequence {ai} of integer…