Key papers in Numerical Analysis
Pofolia’s corpus holds 43 papers from the Numerical Analysis subfield (2012–2022). The list below starts with the most cited.
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”.
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.
Measure Theory and Fine Properties of Functions
2018 · 4,355 citations
This book offers a detailed examination of measure theory in n-dimensional Euclidean space, highlighting the significance of Hausdorff measure and capacity in defining the fine properties of sets and functions.
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.
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.
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.
Stability of Dynamical Systems
2018 · 1,635 citations
A summary is not available for this content.
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.
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.
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.
- 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.
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.
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.
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.
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.
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.
Oscillation Theory for Functional Differential Equations
2017 · 648 citations
This book presents a unified approach to the oscillation theory of functional differential equations, extending techniques from ordinary differential equations.
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.
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.
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.
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.
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.
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.
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.
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.
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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