Most cited papers in Advanced Numerical Analysis Techniques
What are the most cited papers in Advanced Numerical Analysis Techniques?
The most cited paper in Advanced Numerical Analysis Techniques is "Active contours without edges" (Tony Fan-Cheong Chan, Luminita A. Vese, 2001), with 10,394 citations. Next come "UMAP: Uniform Manifold Approximation and Projection" (10,200) and "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement" (6,340).
Showing 50 of 99 papers. Every paper with more than 844 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Active contours without edges Tony Fan-Cheong Chan, Luminita A. Vese · IEEE Transactions on Image Processing | 2001 | 10,394 |
| 2 | UMAP: Uniform Manifold Approximation and Projection Leland McInnes, John Healy, Nathaniel Saul et al. · The Journal of Open Source Software | 2 Sep 2018 | 10,200 |
| 3 | Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Thomas J.R. Hughes, J. Austin Cottrell, Yuri Bazilevs · Computer Methods in Applied Mechanics and Engineering | Feb 2005 | 6,340 |
| 4 | Computational Geometry: Algorithms and Applications Mark de Berg, Otfried Cheong, Marc J. van Kreveld et al. · CERN Document Server (European Organization for Nuclear Research) | 1997 | 4,503 |
| 5 | ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE David H. Douglas, Thomas K. Peucker · Cartographica The International Journal for Geographic Information and Geovisualization | Dec 1973 | 4,256 |
| 6 | On the Statistical Analysis of Dirty Pictures Julian E. Besag · Journal of the Royal Statistical Society Series B (Statistical Methodology) | Jul 1986 | 4,240 |
| 7 | Smoothing noisy data with spline functions Peter G. Craven, Grace Wahba · Numerische Mathematik | Dec 1978 | 3,416 |
| 8 | Affine Invariant Flows in the Beltrami Framework Nir Sochen · Journal of Mathematical Imaging and Vision | 2004 | 3,309 |
| 9 | A level set method for structural topology optimization Michael Yu Wang, Xiaoming Wang, Dongming Guo · Computer Methods in Applied Mechanics and Engineering | 27 Dec 2002 | 3,247 |
| 10 | Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree Holger Wendland · Advances in Computational Mathematics | Dec 1995 | 3,058 |
| 11 | Universal approximation bounds for superpositions of a sigmoidal function Andrew R. Barron · IEEE Transactions on Information Theory | May 1993 | 2,899 |
| 12 | Material interpolation schemes in topology optimization Martin Philip Bendsøe, Ole Sigmund · Archive of Applied Mechanics | 22 Nov 1999 | 2,853 |
| 13 | Occam's inversion; a practical algorithm for generating smooth models from electromagnetic sounding data Steven Constable, Robert L. Parker, Catherine G. Constable · Geophysics | Mar 1987 | 2,797 |
| 14 | Surface reconstruction from unorganized points Hugues Hoppe, Tony DeRose, Tom Duchamp et al. | Jul 1992 | 2,762 |
| 15 | Free-form deformation of solid geometric models Thomas W. Sederberg, Scott R. Parry · ACM SIGGRAPH Computer Graphics | 31 Aug 1986 | 2,599 |
| 16 | Fast Discrete Curvelet Transforms Emmanuel J. Candès, Laurent Demanet, David L. Donoho et al. · Multiscale Modeling and Simulation | 2006 | 2,582 |
| 17 | Thin Plate Regression Splines Simon N. Wood · Journal of the Royal Statistical Society Series B (Statistical Methodology) | 28 Jan 2003 | 2,559 |
| 18 | Spline Functions: Basic Theory. Philip W. Smith, Larry L. Schumaker · Mathematics of Computation | Apr 1982 | 2,505 |
| 19 | Display of surfaces from volume data Marc Levoy · IEEE Computer Graphics and Applications | May 1988 | 2,457 |
| 20 | Method for registration of 3-D shapes Paul J. Besl, Neil David McKay · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE | 30 Apr 1992 | 2,430 |
| 21 | Isogeometric analysis toward integration of CAD and FEA J. Austin Cottrell, Thomas J.R. Hughes, Yuri Bazilevs | 2009 | 2,386 |
| 22 | Screened poisson surface reconstruction Michael Kazhdan, Hugues Hoppe · ACM Transactions on Graphics | Jun 2013 | 2,306 |
| 23 | Smoothing by spline functions Christian H. Reinsch · Numerische Mathematik | Oct 1967 | 2,269 |
| 24 | Curves and Surfaces for Computer Aided Geometric Design--A Practical Guide. Chanderjit Bajaj, Gerald E. Farin · Mathematics of Computation | Oct 1990 | 2,134 |
| 25 | An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications Esteban P. Samaniego, Cosmin Anitescu, Somdatta Goswami et al. · Computer Methods in Applied Mechanics and Engineering | 16 Jan 2020 | 2,096 |
| 26 | A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures Hiroshi Akima · Journal of the ACM | Oct 1970 | 2,093 |
| 27 | Recursively generated B-spline surfaces on arbitrary topological meshes Edwin E. Catmull, J. Clark · Computer-Aided Design | Nov 1978 | 2,027 |
| 28 | The Analysis of the Stability of General Slip Surfaces N. R. Morgenstern, V. E. Price · Géotechnique | Mar 1965 | 2,001 |
| 29 | Radial basis functions theory and implementations Martin Buhmann | 2003 | 1,872 |
| 30 | A signal processing approach to fair surface design Gabriel Taubin | 1995 | 1,870 |
| 31 | On calculating with B-splines Carl de Boor · Journal of Approximation Theory | Jul 1972 | 1,836 |
| 32 | Solving high-dimensional partial differential equations using deep learning Jiequn Han, Arnulf Jentzen, E Weinan · Proceedings of the National Academy of Sciences | 6 Aug 2018 | 1,793 |
| 33 | Fast wavelet transforms and numerical algorithms I Gregory Beylkin, Ronald R. Coifman, Vladimir Abramovich Rokhlin · Communications on Pure and Applied Mathematics | Mar 1991 | 1,784 |
| 34 | An improved illumination model for shaded display Turner Whitted · Communications of the ACM | Jun 1980 | 1,768 |
| 35 | A geometric model for active contours in image processing Vicent Caselles, Francine Catt�, Tomeu Coll et al. · Numerische Mathematik | Dec 1993 | 1,751 |
| 36 | Animating rotation with quaternion curves Ken Shoemake · ACM SIGGRAPH Computer Graphics | Jul 1985 | 1,738 |
| 37 | On the Encoding of Arbitrary Geometric Configurations Herbert Freeman · IEEE Transactions on Electronic Computers | Jun 1961 | 1,673 |
| 38 | Radial basis functions M. D. Buhmann · Acta Numerica | 2000 | 1,661 |
| 39 | Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel S. Sathiya Keerthi, Chih‐Jen Lin · Neural Computation | 3 Jun 2003 | 1,626 |
| 40 | Quasi-Newton Methods, Motivation and Theory John E. Dennis, Jorge J. Morè · SIAM Review | 1977 | 1,569 |
| 41 | Implicit fairing of irregular meshes using diffusion and curvature flow Mathieu Desbrun, Mark Meyer, Peter Schröder et al. | 1999 | 1,552 |
| 42 | The ball-pivoting algorithm for surface reconstruction Fausto Bernardini, Joshua Mittleman, Holly Rushmeier et al. · IEEE Transactions on Visualization and Computer Graphics | Oct 1999 | 1,516 |
| 43 | Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment Zhenyue Zhang, Hongyuan Zha · SIAM Journal on Scientific Computing | 2004 | 1,499 |
| 44 | Metro: Measuring Error on Simplified Surfaces Paolo Cignoni, C. Rocchini, Roberto Scopigno · Computer Graphics Forum | Jun 1998 | 1,492 |
| 45 | Approximation of functional depending on jumps by elliptic functional via t‐convergence Luigi Ambrosio, Vincenzo Maria Tortorelli · Communications on Pure and Applied Mathematics | Dec 1990 | 1,483 |
| 46 | Smoothing noisy data with spline functions Grace Wahba · Numerische Mathematik | Oct 1975 | 1,471 |
| 47 | Gridding with continuous curvature splines in tension Walter H. F. Smith, Paul Wessel · Geophysics | Mar 1990 | 1,465 |
| 48 | The plane with parallel coordinates Alfred Inselberg · The Visual Computer | Aug 1985 | 1,440 |
| 49 | Splines minimizing rotation-invariant semi-norms in Sobolev spaces Jean Duchon · Lecture notes in mathematics | 1977 | 1,394 |
| 50 | An iterative procedure for the polygonal approximation of plane curves Urs Ramer · Computer Graphics and Image Processing | Nov 1972 | 1,388 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.