Numerical Analysis papers

Pofolia’s corpus holds 38 papers from Numerical Analysis (2012–2022), each with a short summary. Below, the 20 most-cited, then the most recently added.

At a glance

• Most cited: Ordinary Differential Equations (2017, 7,323 citations).
• The 20 papers listed have 31,207 citations between them.
• 7 of the 7 with a known journal quartile appeared in a Q1 journal.
• 5 have a free full text (open access).
• Most frequent journals: Society for Industrial and Applied Mathematics eBooks, Acta Numerica, Cambridge University Press eBooks.
• Published between 2012 and 2019.

Most cited

Ranked by citation count. Because citations accumulate over time, this list naturally leans towards work published a few years ago; for where the field is now, see “recently added”. How to read the signals

• Ordinary Differential Equations

  Cambridge University Press eBooks · 2017 · FWCI 378.52 · 7,323 citations

  This handbook offers a collection of self-contained surveys on ordinary differential equations, aiming for accessibility to mathematicians and scientists across various fields.

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• Introductory Lectures on Convex Optimization: A Basic Course

  Medical Entomology and Zoology · 2014 · FWCI 66.94 · 3,724 citations

  This abstract describes the historical development and pedagogical challenges of introducing convex optimization, particularly interior-point methods, to graduate students following Karmarkar's seminal 1980s work.

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• Engineering Optimization Theory and Practice

  2019 · FWCI 49.07 · 3,602 citations

  This abstract outlines a comprehensive textbook covering the theory and practice of engineering optimization, detailing various classical and modern techniques for solving optimization problems.

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• Numerical Methods for Ordinary Differential Equations

  2016 · FWCI 43.60 · 2,940 citations

  This work offers a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods for solving ordinary differential equations.

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• Stability of Dynamical Systems

  2018 · 1,635 citations

  A summary is not available for this content.

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• Derivative-free optimization: a review of algorithms and comparison of software implementations

  Journal of Global Optimization · 2012 · Q1 · FWCI 57.31 · 1,262 citations · Open access

  This review systematically compares 22 derivative-free optimization software implementations on 502 problems, finding that specific solvers like 'nlsSolve', 'nlopt', and 'nomad' generally outperform others in finding near-global solutions and refining optima.

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• Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems

  SIAM Journal on Optimization · 2012 · Q1 · SJR 1.00 · FWCI 126.91 · 1,250 citations

  New coordinate descent methods using random partial updates significantly improve efficiency for huge-scale optimization problems, outperforming standard deterministic algorithms in certain cases.

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• JuMP: A Modeling Language for Mathematical Optimization

  SIAM Review · 2017 · Q1 · SJR 2.00 · FWCI 101.57 · 1,228 citations

  JuMP is a new open-source modeling language for mathematical optimization problems, offering high-level algebraic syntax and performance comparable to commercial tools.

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• - Nonlinear Ordinary Differential Equations

  2013 · FWCI 108.15 · 1,212 citations

  These notes focus on nonlinear ordinary differential equations, emphasizing the physical relevance of solutions and the importance of stability for equilibrium points.

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• Time‐Dependent Problems and Difference Methods

  2013 · FWCI 14.83 · 909 citations

  This book provides a self-contained treatment of difference methods for approximating solutions to time-dependent partial differential equations.

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• Introduction to algorithms

  Cambridge University Press eBooks · 2018 · FWCI 146.45 · 818 citations

  This textbook offers an accessible introduction to convex optimization, emphasizing practical understanding and real-world application over complex mathematical details.

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• Hamiltonian Simulation by Qubitization

  Quantum · 2019 · Q1 · SJR 2.00 · FWCI 63.22 · 808 citations · Open access

  A new quantum algorithm, 'qubitization', enables Hamiltonian simulation with optimal query complexity and low overhead, improving precision simulations quadratically.

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• ECOS: An SOCP solver for embedded systems

  2013 · 729 citations

  ECOS is a new, compact, and efficient interior-point solver for second-order cone programming (SOCP) specifically designed for embedded systems.

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• Mixed-integer nonlinear optimization

  Acta Numerica · 2013 · Q1 · SJR 5.00 · FWCI 39.75 · 691 citations

  This review surveys methods for solving mixed-integer nonlinear programming (MINLP) problems, which combine discrete decisions with nonlinear system dynamics, a common challenge in scientific, engineering, and public sector applications.

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• High-dimensional integration: The quasi-Monte Carlo way

  Acta Numerica · 2013 · Q1 · SJR 5.00 · FWCI 55.12 · 635 citations

  This review surveys recent advances in quasi-Monte Carlo (QMC) methods, which use equal-weight rules to approximate high-dimensional integrals over the unit cube.

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• Linear and Nonlinear Functional Analysis with Applications

  Society for Industrial and Applied Mathematics eBooks · 2013 · FWCI 8.87 · 573 citations

  This textbook provides a comprehensive introduction to linear and nonlinear functional analysis, featuring self-contained proofs and numerous applications to partial differential equations, numerical analysis, and optimization.

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• Semidefinite Optimization and Convex Algebraic Geometry

  Society for Industrial and Applied Mathematics eBooks · 2012 · FWCI 5.47 · 488 citations

  This book offers an accessible introduction to convex algebraic geometry, a field merging semidefinite programming with polynomial optimization, drawing from convex geometry, algebraic geometry, and optimization.

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• CVXPY: A Python-Embedded Modeling Language for Convex Optimization

  arXiv (Cornell University) · 2016 · 477 citations · Open access

  CVXPY is a new Python-embedded language that allows users to express convex optimization problems using natural mathematical syntax, bypassing the need for restrictive standard forms.

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• whfast: a fast and unbiased implementation of a symplectic Wisdom–Holman integrator for long-term gravitational simulations

  Monthly Notices of the Royal Astronomical Society · 2015 · Q1 · SJR 1.00 · FWCI 33.32 · 465 citations · Open access

  whfast, a new Wisdom–Holman symplectic integrator, achieves significantly faster and more energy-conserving long-term gravitational simulations by improving Kepler solvers and coordinate transformations, removing secular energy errors.

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• Practical Augmented Lagrangian Methods for Constrained Optimization

  Society for Industrial and Applied Mathematics eBooks · 2014 · FWCI 4.07 · 438 citations · Open access

  This book presents Augmented Lagrangian methods for solving practical constrained optimization problems, emphasizing convergence theory and practical algorithmic behavior.

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Recently added

• Partial Differential Equations

  2022 · 254 citations

  Most real-world physical and engineering systems are modeled by coupled, nonlinear partial differential equations (PDEs) that lack analytical solutions, necessitating numerical methods for practical problem-solving.

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• Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes

  SIAM Review · 2021 · Q1 · SJR 2.00 · FWCI 49.43 · 262 citations

  New maximum bound principles are derived for a class of semilinear parabolic equations, enabling the development of stable exponential time-differencing (ETD) schemes that avoid restrictive time-step limitations.

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• Engineering Optimization Theory and Practice

  2019 · FWCI 49.07 · 3,602 citations

  This abstract outlines a comprehensive textbook covering the theory and practice of engineering optimization, detailing various classical and modern techniques for solving optimization problems.

  Go to source →

• Hamiltonian Simulation by Qubitization

  Quantum · 2019 · Q1 · SJR 2.00 · FWCI 63.22 · 808 citations · Open access

  A new quantum algorithm, 'qubitization', enables Hamiltonian simulation with optimal query complexity and low overhead, improving precision simulations quadratically.

  Go to source →

• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation

  SIAM Journal on Numerical Analysis · 2019 · Q1 · SJR 2.00 · FWCI 29.13 · 282 citations

  New first and second order exponential time differencing schemes unconditionally preserve the discrete maximum principle for the nonlocal Allen--Cahn equation.

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• A review and comparison of solvers for convex MINLP

  Optimization and Engineering · 2018 · Q2 · FWCI 36.91 · 299 citations · Open access

  This review compares 17 deterministic solvers for convex Mixed-Integer Non-Linear Programming (MINLP) problems using 335 instances from MINLPLib, finding that solver performance varies significantly based on problem characteristics like nonlinearity and discrete variable proportion.

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• Stability of Dynamical Systems

  2018 · 1,635 citations

  A summary is not available for this content.

  Go to source →

• Introduction to algorithms

  Cambridge University Press eBooks · 2018 · FWCI 146.45 · 818 citations

  This textbook offers an accessible introduction to convex optimization, emphasizing practical understanding and real-world application over complex mathematical details.

  Go to source →

Journals in this field

The journals that publish most of this field’s papers. Quartile (Q1–Q4), SJR and h-index are from SCImago Journal Rank; “in this field” is how many of the journal’s pooled papers belong here. What is a Q1 journal? · What is the h-index?

Every journal in Numerical Analysis (Q1–Q4) →

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