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## Vershynin, Roman

Compute Distance To:
 Author ID: vershynin.roman Published as: Vershynin, Roman; Vershynin, R.; Vershinin, R. V.; Vershynin, R. V. more...less Homepage: http://www-personal.umich.edu/~romanv/ External Links: MGP · ResearchGate · Math-Net.Ru
 Documents Indexed: 75 Publications since 1998, including 1 Book Co-Authors: 41 Co-Authors with 53 Joint Publications 1,043 Co-Co-Authors
all top 5

### Co-Authors

 22 single-authored 17 Rudelson, Mark 8 Plan, Yaniv 4 Levina, Elizaveta 3 Baldi, Pierre 3 Le, Can Minh 3 Mendelson, Shahar 3 Strohmer, Thomas 3 Tomczak-Jaegermann, Nicole 2 Casazza, Peter George 2 Litvak, Aleksandr Evgen’evich 2 Pajor, Alain 1 Ai, Albert 1 Banks, Jess 1 Christensen, Ole 1 Diestel, Joseph 1 Farrell, Brendan 1 Gilbert, Anna C. 1 Giryes, Raja 1 Godefroy, Gilles 1 Guédon, Olivier 1 Kadets, Vladimir M. 1 Klartag, Bo’az 1 Lapanowski, Alex 1 Liaw, Christopher 1 Lindner, Alexander M. 1 Livshyts, Galyna V. 1 Lyubarskii, Yurii I. 1 Mehrabian, Abbas 1 Moore, Cristopher 1 Needell, Deanna 1 Pełczyński, Aleksander 1 Rebrova, Elizaveta 1 Schechtman, Gideon 1 Srivastava, Nikhil 1 Strauss, Martin J. 1 Tan, Yan Shuo 1 Tikhomirov, Konstantin E. 1 Tropp, Joel A. 1 Verzelen, Nicolas 1 Xu, Jiaming 1 Yudovina, Elena
all top 5

### Serials

 5 IEEE Transactions on Information Theory 3 Communications on Pure and Applied Mathematics 3 Israel Journal of Mathematics 3 Advances in Mathematics 3 The Annals of Probability 3 Probability Theory and Related Fields 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Random Structures & Algorithms 2 IMRN. International Mathematics Research Notices 2 Geometric and Functional Analysis. GAFA 2 The Journal of Fourier Analysis and Applications 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Information and Inference 2 SIAM Journal on Mathematics of Data Science 1 Studia Mathematica 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 The Annals of Statistics 1 Archiv der Mathematik 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Quaestiones Mathematicae 1 SIAM Journal on Computing 1 Rendiconti. Scienze Matemàtiche e Applicazioni. A 1 Discrete & Computational Geometry 1 Journal of Theoretical Probability 1 Journal of the American Mathematical Society 1 Neural Networks 1 Acta Mathematica Universitatis Comenianae. New Series 1 Linear Algebra and its Applications 1 Notices of the American Mathematical Society 1 Russian Mathematics 1 Applied and Computational Harmonic Analysis 1 Matematicheskaya Fizika, Analiz, Geometriya 1 Electronic Communications in Probability 1 Bernoulli 1 Journal of the ACM 1 Annals of Mathematics. Second Series 1 Foundations of Computational Mathematics 1 Journal of Statistical Mechanics: Theory and Experiment 1 Cambridge Series in Statistical and Probabilistic Mathematics
all top 5

### Fields

 31 Probability theory and stochastic processes (60-XX) 22 Functional analysis (46-XX) 15 Information and communication theory, circuits (94-XX) 13 Computer science (68-XX) 12 Convex and discrete geometry (52-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 9 Statistics (62-XX) 6 Numerical analysis (65-XX) 6 Operations research, mathematical programming (90-XX) 4 Combinatorics (05-XX) 3 Operator theory (47-XX) 2 Approximations and expansions (41-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Quantum theory (81-XX)

### Citations contained in zbMATH Open

65 Publications have been cited 1,804 times in 1,265 Documents Cited by Year
A randomized Kaczmarz algorithm with exponential convergence. Zbl 1169.68052
Strohmer, Thomas; Vershynin, Roman
2009
High-dimensional probability. An introduction with applications in data science. Zbl 1430.60005
Vershynin, Roman
2018
The Littlewood-Offord problem and invertibility of random matrices. Zbl 1139.15015
Rudelson, Mark; Vershynin, Roman
2008
On sparse reconstruction from Fourier and Gaussian measurements. Zbl 1149.94010
Rudelson, Mark; Vershynin, Roman
2008
Hanson-Wright inequality and sub-Gaussian concentration. Zbl 1329.60056
Rudelson, Mark; Vershynin, Roman
2013
Smallest singular value of a random rectangular matrix. Zbl 1183.15031
Rudelson, Mark; Vershynin, Roman
2009
Non-asymptotic theory of random matrices: extreme singular values. Zbl 1227.60011
Rudelson, Mark; Vershynin, Roman
2011
Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Zbl 1183.68739
Needell, Deanna; Vershynin, Roman
2009
Invertibility of symmetric random matrices. Zbl 1291.15088
Vershynin, Roman
2014
Robust 1-bit compressed sensing and sparse logistic regression: a convex programming approach. Zbl 1364.94153
Plan, Yaniv; Vershynin, Roman
2013
One-bit compressed sensing by linear programming. Zbl 1335.94018
Plan, Yaniv; Vershynin, Roman
2013
Sampling from large matrices: an approach through geometric functional analysis. Zbl 1326.68333
Rudelson, Mark; Vershynin, Roman
2007
How close is the sample covariance matrix to the actual covariance matrix? Zbl 1365.62208
Vershynin, Roman
2012
Frames and the Feichtinger conjecture. Zbl 1082.46018
Casazza, Peter G.; Christensen, Ole; Lindner, Alexander M.; Vershynin, Roman
2005
Community detection in sparse networks via Grothendieck’s inequality. Zbl 1357.90111
Guédon, Olivier; Vershynin, Roman
2016
Concentration and regularization of random graphs. Zbl 1373.05179
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2017
Delocalization of eigenvectors of random matrices with independent entries. Zbl 1352.60007
Rudelson, Mark; Vershynin, Roman
2015
Spectral norm of products of random and deterministic matrices. Zbl 1235.60009
Vershynin, Roman
2011
Small ball probability and Dvoretzky’s Theorem. Zbl 1120.46003
Klartag, B.; Vershynin, R.
2007
Geometric approach to error-correcting codes and reconstruction of signals. Zbl 1103.94014
Rudelson, Mark; Vershynin, Roman
2005
Entropy and the combinatorial dimension. Zbl 1039.60016
Mendelson, S.; Vershynin, R.
2003
John’s decompositions: Selecting a large part. Zbl 0998.46006
Vershynin, R.
2001
Covariance estimation for distributions with $${2+\varepsilon}$$ moments. Zbl 1293.62121
Srivastava, Nikhil; Vershynin, Roman
2013
No-gaps delocalization for general random matrices. Zbl 1375.60027
Rudelson, Mark; Vershynin, Roman
2016
Small ball probabilities for linear images of high-dimensional distributions. Zbl 1330.60029
Rudelson, Mark; Vershynin, Roman
2015
Dimension reduction by random hyperplane tessellations. Zbl 1296.52014
Plan, Yaniv; Vershynin, Roman
2014
The generalized lasso with non-linear observations. Zbl 1359.94153
Plan, Yaniv; Vershynin, Roman
2016
One-bit compressed sensing with non-Gaussian measurements. Zbl 1332.94041
Ai, Albert; Lapanowski, Alex; Plan, Yaniv; Vershynin, Roman
2014
The least singular value of a random square matrix is O$$(n ^{- 1/2})$$. Zbl 1152.60042
Rudelson, Mark; Vershynin, Roman
2008
One sketch for all: fast algorithms for compressed sensing. Zbl 1232.94008
Gilbert, A. C.; Strauss, M. J.; Tropp, J. A.; Vershynin, R.
2007
Combinatorics of random processes and sections of convex bodies. Zbl 1114.60009
Rudelson, M.; Vershynin, R.
2006
Phase retrieval via randomized Kaczmarz: theoretical guarantees. Zbl 1476.90224
Tan, Yan Shuo; Vershynin, Roman
2019
Invertibility of random matrices: unitary and orthogonal perturbations. Zbl 1290.60007
Rudelson, Mark; Vershynin, Roman
2014
High-dimensional estimation with geometric constraints. Zbl 1383.62121
Plan, Y.; Vershynin, R.; Yudovina, E.
2017
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization. Zbl 1401.94065
Banks, Jess; Moore, Cristopher; Vershynin, Roman; Verzelen, Nicolas; Xu, Jiaming
2018
Uncertainty principles and vector quantization. Zbl 1366.94117
Lyubarskii, Yurii; Vershynin, Roman
2010
A randomized solver for linear systems with exponential convergence. Zbl 1155.65323
Strohmer, Thomas; Vershynin, Roman
2006
Estimation in high dimensions: a geometric perspective. Zbl 1370.94269
Vershynin, Roman
2015
Beyond Hirsch conjecture: walks on random polytopes and smoothed complexity of the simplex method. Zbl 1200.68128
Vershynin, Roman
2009
Partial estimation of covariance matrices. Zbl 1318.62179
Levina, Elizaveta; Vershynin, Roman
2012
Concentration inequalities for random tensors. Zbl 1472.60041
Vershynin, Roman
2020
The smallest singular value of inhomogeneous square random matrices. Zbl 1467.60010
Livshyts, Galyna V.; Tikhomirov, Konstantin; Vershynin, Roman
2021
Isoperimetry of waists and local versus global asymptotic convex geometries. Zbl 1103.46008
Vershynin, Roman
2006
Random Euclidean embeddings in spaces of bounded volume ratio. Zbl 1049.46007
Litvak, Alexander; Pajor, Alain; Rudelson, Mark; Tomczak-Jaegermann, Nicole; Vershynin, Roman
2004
Comments on the randomized Kaczmarz method. Zbl 1177.68253
Strohmer, Thomas; Vershynin, Roman
2009
On the effective measure of dimension in the analysis cosparse model. Zbl 1359.94032
Giryes, Raja; Plan, Yaniv; Vershynin, Roman
2015
Optimization via low-rank approximation for community detection in networks. Zbl 1331.62312
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2016
Euclidean embeddings in spaces of finite volume ratio via random matrices. Zbl 1090.52002
Litvak, A. E.; Pajor, A.; Rudelson, M.; Tomczak-Jaegermann, N.; Vershynin, R.
2005
A simple tool for bounding the deviation of random matrices on geometric sets. Zbl 1366.60011
Liaw, Christopher; Mehrabian, Abbas; Plan, Yaniv; Vershynin, Roman
2017
Random sets of isomorphism of linear operators on Hilbert space. Zbl 1129.46006
Vershynin, Roman
2006
Smoothed analysis of symmetric random matrices with continuous distributions. Zbl 1335.60007
Farrell, Brendan; Vershynin, Roman
2016
Approximating the moments of marginals of high-dimensional distributions. Zbl 1271.62122
Vershynin, Roman
2011
Norms of random matrices: local and global problems. Zbl 1380.60016
Rebrova, Elizaveta; Vershynin, Roman
2018
Frame expansions with erasures: an approach through the non-commutative operator theory. Zbl 1070.94005
Vershynin, Roman
2005
On large random almost euclidean bases. Zbl 0982.46005
Vershynin, R.
2000
Entropy, combinatorial dimensions and random averages. Zbl 1050.68071
Mendelson, Shahar; Vershynin, Roman
2002
The capacity of feedforward neural networks. Zbl 1434.68498
Baldi, Pierre; Vershynin, Roman
2019
Remarks on the geometry of coordinate projections in $$\mathbb{R}^n$$. Zbl 1066.46009
Mendelson, S.; Vershynin, R.
2004
Subsequences of frames. Zbl 0987.46028
Vershynin, R.
2001
Concentration of random graphs and application to community detection. Zbl 1448.05179
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2018
Embedding Levy families into Banach spaces. Zbl 1012.46013
Rudelson, M.; Vershynin, R.
2002
A tribute to Nigel J. Kalton (1946–2010). Zbl 1284.01055
Pelczyński, Aleksander; Diestel, Joe; Vershynin, Roman; Godefroy, Gilles
2012
Absolutely representing systems, uniform smoothness and type. Zbl 0977.46003
Vershynin, R.
2000
Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms. Zbl 1173.90476
Vershynin, Roman
2007
Integer cells in convex sets. Zbl 1084.52005
Vershynin, R.
2005
The smallest singular value of inhomogeneous square random matrices. Zbl 1467.60010
Livshyts, Galyna V.; Tikhomirov, Konstantin; Vershynin, Roman
2021
Concentration inequalities for random tensors. Zbl 1472.60041
Vershynin, Roman
2020
Phase retrieval via randomized Kaczmarz: theoretical guarantees. Zbl 1476.90224
Tan, Yan Shuo; Vershynin, Roman
2019
The capacity of feedforward neural networks. Zbl 1434.68498
Baldi, Pierre; Vershynin, Roman
2019
High-dimensional probability. An introduction with applications in data science. Zbl 1430.60005
Vershynin, Roman
2018
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization. Zbl 1401.94065
Banks, Jess; Moore, Cristopher; Vershynin, Roman; Verzelen, Nicolas; Xu, Jiaming
2018
Norms of random matrices: local and global problems. Zbl 1380.60016
Rebrova, Elizaveta; Vershynin, Roman
2018
Concentration of random graphs and application to community detection. Zbl 1448.05179
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2018
Concentration and regularization of random graphs. Zbl 1373.05179
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2017
High-dimensional estimation with geometric constraints. Zbl 1383.62121
Plan, Y.; Vershynin, R.; Yudovina, E.
2017
A simple tool for bounding the deviation of random matrices on geometric sets. Zbl 1366.60011
Liaw, Christopher; Mehrabian, Abbas; Plan, Yaniv; Vershynin, Roman
2017
Community detection in sparse networks via Grothendieck’s inequality. Zbl 1357.90111
Guédon, Olivier; Vershynin, Roman
2016
No-gaps delocalization for general random matrices. Zbl 1375.60027
Rudelson, Mark; Vershynin, Roman
2016
The generalized lasso with non-linear observations. Zbl 1359.94153
Plan, Yaniv; Vershynin, Roman
2016
Optimization via low-rank approximation for community detection in networks. Zbl 1331.62312
Le, Can M.; Levina, Elizaveta; Vershynin, Roman
2016
Smoothed analysis of symmetric random matrices with continuous distributions. Zbl 1335.60007
Farrell, Brendan; Vershynin, Roman
2016
Delocalization of eigenvectors of random matrices with independent entries. Zbl 1352.60007
Rudelson, Mark; Vershynin, Roman
2015
Small ball probabilities for linear images of high-dimensional distributions. Zbl 1330.60029
Rudelson, Mark; Vershynin, Roman
2015
Estimation in high dimensions: a geometric perspective. Zbl 1370.94269
Vershynin, Roman
2015
On the effective measure of dimension in the analysis cosparse model. Zbl 1359.94032
Giryes, Raja; Plan, Yaniv; Vershynin, Roman
2015
Invertibility of symmetric random matrices. Zbl 1291.15088
Vershynin, Roman
2014
Dimension reduction by random hyperplane tessellations. Zbl 1296.52014
Plan, Yaniv; Vershynin, Roman
2014
One-bit compressed sensing with non-Gaussian measurements. Zbl 1332.94041
Ai, Albert; Lapanowski, Alex; Plan, Yaniv; Vershynin, Roman
2014
Invertibility of random matrices: unitary and orthogonal perturbations. Zbl 1290.60007
Rudelson, Mark; Vershynin, Roman
2014
Hanson-Wright inequality and sub-Gaussian concentration. Zbl 1329.60056
Rudelson, Mark; Vershynin, Roman
2013
Robust 1-bit compressed sensing and sparse logistic regression: a convex programming approach. Zbl 1364.94153
Plan, Yaniv; Vershynin, Roman
2013
One-bit compressed sensing by linear programming. Zbl 1335.94018
Plan, Yaniv; Vershynin, Roman
2013
Covariance estimation for distributions with $${2+\varepsilon}$$ moments. Zbl 1293.62121
Srivastava, Nikhil; Vershynin, Roman
2013
How close is the sample covariance matrix to the actual covariance matrix? Zbl 1365.62208
Vershynin, Roman
2012
Partial estimation of covariance matrices. Zbl 1318.62179
Levina, Elizaveta; Vershynin, Roman
2012
A tribute to Nigel J. Kalton (1946–2010). Zbl 1284.01055
Pelczyński, Aleksander; Diestel, Joe; Vershynin, Roman; Godefroy, Gilles
2012
Non-asymptotic theory of random matrices: extreme singular values. Zbl 1227.60011
Rudelson, Mark; Vershynin, Roman
2011
Spectral norm of products of random and deterministic matrices. Zbl 1235.60009
Vershynin, Roman
2011
Approximating the moments of marginals of high-dimensional distributions. Zbl 1271.62122
Vershynin, Roman
2011
Uncertainty principles and vector quantization. Zbl 1366.94117
Lyubarskii, Yurii; Vershynin, Roman
2010
A randomized Kaczmarz algorithm with exponential convergence. Zbl 1169.68052
Strohmer, Thomas; Vershynin, Roman
2009
Smallest singular value of a random rectangular matrix. Zbl 1183.15031
Rudelson, Mark; Vershynin, Roman
2009
Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Zbl 1183.68739
Needell, Deanna; Vershynin, Roman
2009
Beyond Hirsch conjecture: walks on random polytopes and smoothed complexity of the simplex method. Zbl 1200.68128
Vershynin, Roman
2009
Comments on the randomized Kaczmarz method. Zbl 1177.68253
Strohmer, Thomas; Vershynin, Roman
2009
The Littlewood-Offord problem and invertibility of random matrices. Zbl 1139.15015
Rudelson, Mark; Vershynin, Roman
2008
On sparse reconstruction from Fourier and Gaussian measurements. Zbl 1149.94010
Rudelson, Mark; Vershynin, Roman
2008
The least singular value of a random square matrix is O$$(n ^{- 1/2})$$. Zbl 1152.60042
Rudelson, Mark; Vershynin, Roman
2008
Sampling from large matrices: an approach through geometric functional analysis. Zbl 1326.68333
Rudelson, Mark; Vershynin, Roman
2007
Small ball probability and Dvoretzky’s Theorem. Zbl 1120.46003
Klartag, B.; Vershynin, R.
2007
One sketch for all: fast algorithms for compressed sensing. Zbl 1232.94008
Gilbert, A. C.; Strauss, M. J.; Tropp, J. A.; Vershynin, R.
2007
Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms. Zbl 1173.90476
Vershynin, Roman
2007
Combinatorics of random processes and sections of convex bodies. Zbl 1114.60009
Rudelson, M.; Vershynin, R.
2006
A randomized solver for linear systems with exponential convergence. Zbl 1155.65323
Strohmer, Thomas; Vershynin, Roman
2006
Isoperimetry of waists and local versus global asymptotic convex geometries. Zbl 1103.46008
Vershynin, Roman
2006
Random sets of isomorphism of linear operators on Hilbert space. Zbl 1129.46006
Vershynin, Roman
2006
Frames and the Feichtinger conjecture. Zbl 1082.46018
Casazza, Peter G.; Christensen, Ole; Lindner, Alexander M.; Vershynin, Roman
2005
Geometric approach to error-correcting codes and reconstruction of signals. Zbl 1103.94014
Rudelson, Mark; Vershynin, Roman
2005
Euclidean embeddings in spaces of finite volume ratio via random matrices. Zbl 1090.52002
Litvak, A. E.; Pajor, A.; Rudelson, M.; Tomczak-Jaegermann, N.; Vershynin, R.
2005
Frame expansions with erasures: an approach through the non-commutative operator theory. Zbl 1070.94005
Vershynin, Roman
2005
Integer cells in convex sets. Zbl 1084.52005
Vershynin, R.
2005
Random Euclidean embeddings in spaces of bounded volume ratio. Zbl 1049.46007
Litvak, Alexander; Pajor, Alain; Rudelson, Mark; Tomczak-Jaegermann, Nicole; Vershynin, Roman
2004
Remarks on the geometry of coordinate projections in $$\mathbb{R}^n$$. Zbl 1066.46009
Mendelson, S.; Vershynin, R.
2004
Entropy and the combinatorial dimension. Zbl 1039.60016
Mendelson, S.; Vershynin, R.
2003
Entropy, combinatorial dimensions and random averages. Zbl 1050.68071
Mendelson, Shahar; Vershynin, Roman
2002
Embedding Levy families into Banach spaces. Zbl 1012.46013
Rudelson, M.; Vershynin, R.
2002
John’s decompositions: Selecting a large part. Zbl 0998.46006
Vershynin, R.
2001
Subsequences of frames. Zbl 0987.46028
Vershynin, R.
2001
On large random almost euclidean bases. Zbl 0982.46005
Vershynin, R.
2000
Absolutely representing systems, uniform smoothness and type. Zbl 0977.46003
Vershynin, R.
2000
all top 5

### Cited by 1,786 Authors

 31 Vershynin, Roman 27 Needell, Deanna 19 Mendelson, Shahar 19 Rauhut, Holger 19 Tikhomirov, Konstantin E. 18 Litvak, Aleksandr Evgen’evich 18 Paouris, Grigoris 18 Tomczak-Jaegermann, Nicole 18 Vu, Van H. 17 Rudelson, Mark 16 Krahmer, Felix 14 Götze, Friedrich 13 Mixon, Dustin G. 12 Guédon, Olivier 12 Nguyen, Hoi H. 12 Ward, Rachel A. 11 Bandeira, Afonso S. 11 Casazza, Peter George 11 Pajor, Alain 11 Tropp, Joel A. 10 Jain, Vishesh 10 Saab, Rayan 10 Tao, Terence 10 Youssef, Pierre 9 Chafaï, Djalil 9 Iwen, Mark A. 9 Wu, Wenting 8 Adamczak, Radosław 8 Bordenave, Charles 8 Chen, Xuemei 8 Fan, Jianqing 8 Levina, Elizaveta 8 Lytova, Anna 8 O’Rourke, Sean D. 8 Richtárik, Peter 8 Valettas, Petros 7 Bai, Zhongzhi 7 Fornasier, Massimo 7 Li, Song 7 Luh, Kyle 7 Pivovarov, Peter 7 Speegle, Darrin M. 7 Zaitsev, Andrei Yu. 6 Cai, Jian-Feng 6 Candès, Emmanuel J. 6 Dirksen, Sjoerd 6 Fadili, Jalal M. 6 Friedland, Omer 6 Giannopoulos, Apostolos A. 6 Haddock, Jamie 6 Kolchinskiĭ, Vladimir I’ich 6 Li, Weiguo 6 Lopatto, Patrick 6 Ma, Anna 6 Priebe, Carey E. 6 Rebrova, Elizaveta 6 Sabelfeld, Karl Karlovich 6 Temlyakov, Vladimir Nikolaevich 6 Weber, Eric S. 6 Wu, Nianci 5 Amini, Arash Ali 5 Bahmani, Sohail 5 Bao, Wendi 5 Basak, Anirban 5 Bownik, Marcin 5 Cai, Tony Tony 5 Drineas, Petros 5 Eliseeva, Yulia S. 5 Fickus, Matthew C. 5 Foucart, Simon 5 Fu, Fangwei 5 Güntürk, Cemalettin Sinan 5 Huang, Meng 5 Lecué, Guillaume 5 Mahoney, Michael W. 5 Peyré, Gabriel 5 Powell, Alexander M. 5 Steinerberger, Stefan 5 Strohmer, Thomas 5 Tikhomirov, Alexander Nikolaevich 5 Tsolomitis, Antonis 5 Wang, Rongrong 5 Woodruff, David P. 5 Xiu, Dongbin 5 Zeitouni, Ofer 4 Abbe, Emmanuel 4 Barvinok, Alexander I. 4 Benaych-Georges, Florent 4 Benigni, Lucas 4 Chen, Xiaohui 4 Ergür, Alperen Ali 4 Gower, Robert Mansel 4 Han, Deguang 4 Jin, Bangti 4 Krüger, Torben 4 Kutyniok, Gitta 4 Liu, Han 4 Livshyts, Galyna V. 4 Lu, Xiliang 4 Molitor, Denali ...and 1,686 more Authors
all top 5

### Cited in 271 Serials

 58 Applied and Computational Harmonic Analysis 51 Electronic Journal of Statistics 49 The Annals of Statistics 37 Journal of Machine Learning Research (JMLR) 35 Linear Algebra and its Applications 33 Probability Theory and Related Fields 29 The Annals of Probability 24 Bernoulli 23 SIAM Journal on Matrix Analysis and Applications 20 The Journal of Fourier Analysis and Applications 19 Mathematical Programming. Series A. Series B 19 Foundations of Computational Mathematics 17 Advances in Mathematics 16 Israel Journal of Mathematics 16 Journal of Computational and Applied Mathematics 16 SIAM Journal on Optimization 16 SIAM Journal on Scientific Computing 15 SIAM Journal on Mathematics of Data Science 14 Journal of Multivariate Analysis 14 Electronic Journal of Probability 13 Journal of Functional Analysis 13 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 13 SIAM Journal on Imaging Sciences 12 Discrete & Computational Geometry 12 Journal of Theoretical Probability 12 Numerical Algorithms 11 Inverse Problems 11 Journal of Complexity 11 The Annals of Applied Probability 11 Random Matrices: Theory and Applications 11 Information and Inference 10 Mathematics of Computation 10 Proceedings of the American Mathematical Society 10 SIAM Journal on Computing 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Constructive Approximation 9 Machine Learning 8 Journal of Mathematical Analysis and Applications 8 Applied Mathematics and Computation 8 Circuits, Systems, and Signal Processing 8 Random Structures & Algorithms 7 Communications in Mathematical Physics 7 Journal of the American Statistical Association 7 Journal of Econometrics 7 Mathematics of Operations Research 7 Geometric and Functional Analysis. GAFA 7 Computational Optimization and Applications 6 Communications on Pure and Applied Mathematics 6 BIT 6 Transactions of the American Mathematical Society 6 Statistical Science 6 Journal of Mathematical Sciences (New York) 6 Science China. Mathematics 5 Journal of Computational Physics 5 Duke Mathematical Journal 5 Journal of Approximation Theory 5 Applied Numerical Mathematics 5 Applied Mathematics Letters 5 Stochastic Processes and their Applications 5 Computational Statistics and Data Analysis 5 Combinatorics, Probability and Computing 5 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 5 Communications in Contemporary Mathematics 4 Journal of Mathematical Physics 4 Theoretical Computer Science 4 Statistics & Probability Letters 4 Journal of the American Mathematical Society 4 SIAM Review 4 Applied Mathematics. Series B (English Edition) 4 Monte Carlo Methods and Applications 4 Electronic Communications in Probability 4 Journal of the European Mathematical Society (JEMS) 4 Analysis and Applications (Singapore) 4 Computational & Mathematical Methods in Medicine 3 Discrete Applied Mathematics 3 Journal of Mathematical Biology 3 Journal of Statistical Physics 3 Theory of Probability and its Applications 3 Automatica 3 Calcolo 3 Journal of Optimization Theory and Applications 3 Journal of Statistical Planning and Inference 3 Mathematische Annalen 3 Mathematika 3 Numerische Mathematik 3 Operations Research 3 Acta Applicandae Mathematicae 3 Neural Networks 3 Signal Processing 3 Neural Computation 3 Bulletin of the American Mathematical Society. New Series 3 International Journal of Wavelets, Multiresolution and Information Processing 3 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 3 Probability Surveys 3 Science China. Information Sciences 3 Forum of Mathematics, Sigma 3 East Asian Journal on Applied Mathematics 3 Mathematical Statistics and Learning 3 Electronic Research Archive 3 Sampling Theory, Signal Processing, and Data Analysis ...and 171 more Serials
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### Cited in 54 Fields

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## What Is Operating Income?

Operating income is an accounting figure that measures the amount of profit realized from a business's operations, after deducting operating expenses such as?wages, depreciation, and cost of goods sold?(COGS).

Operating incomealso called income from operationstakes a company's gross income, which is equivalent to total revenue minus COGS, and subtracts all operating expenses. A business's operating expenses are costs incurred from normal?operating activities and include items such as office supplies and utilities.

### Key Takeaways

• Operating income reports the amount of profit realized from a business's ongoing operations.
• Operating income takes a company's gross income, which is equivalent to total revenue minus cost of goods sold (COGS), and subtracts all operating expenses.
• Analyzing operating income is helpful to investors because it doesn't include taxes and other one-off items that may skew a company's profit in a given year.
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## Understanding Operating Income

Operating income is a measurement that shows how much of a company's revenue will eventually become profits. Operating income is similar to?a company's?earnings before interest and taxes?(EBIT); it is also referred to as the operating profit or recurring profit. The one big difference between operating income and EBIT is that EBIT includes any non-operating?income the company generates.

Analyzing operating income is helpful to investors because it doesn't include taxes and other one-off items that might skew profit or net income. A company that's generating an increasing amount of operating income is seen as favorable because it means that the company's management is generating more revenue while controlling expenses, production costs, and overhead.

## How to Calculate Operating Income

The operating income formula is outlined below:

?$\text{Operating Income} = \text{Gross Income} - \text{Operating Expenses}$?

Operating expenses include?selling, general, and administrative expense (SG&A), depreciation,?and amortization, and other operating expenses. Operating?income excludes items such as investments in other firms?(non-operating income), taxes,?and interest expenses. In addition, nonrecurring items, such as cash paid for a lawsuit settlement, are not included. Operating income is required to calculate the?operating margin, which describes a company's operating efficiency.

Operating income is the amount of income a company generates from its core operations, meaning it excludes any income and expenses not directly tied to the core business.

## Operating Income?Examples

Many companies focus on operating income when measuring the operational success of the business. For example, Company ABC, a hospital and drug firm, reports an operating income rise by 20% year-over-year to $25 million during the?first two quarters of its fiscal year. The company realized an increase in revenue and operating income?due to an increase in patient volume over the two quarters. The rise in patient visits was driven by two of the company's new immunotherapy drugs: One drug treats lung cancer and the other drug treats melanoma. In another example, we have Company Red, which reports financial results for the first quarter of its fiscal year. The company saw operating income rise by 37%, when compared with the same period in the previous year. The report of the increase in operating income is especially important because the company is looking to merge with Company Blue, and shareholders are slated to vote on the potential merger next month. While Company Red's?first-quarter sales did fall by 3%, its operating income growth could potentially give Company Blue shareholders confidence in voting to merge the two companies. ### How to Find Operating Income The example below highlights how to find and calculate operating income using the income statement for Apple (AAPL). The figures are from the quarter ending June 29, 2019.?? • Operating income for June 2019 was$11.5 billion (highlighted in green).
• Operating income is calculated before, or located slightly above, net income.
• We can see that operating income is the result of gross incomeor gross margin on Apple's income statementof $20.2 billion minus operating expenses of$8.6 billion.??

It's important to note that operating income is different than net income (as well as gross profit). Operating income includes more expense line items than gross profit, which primarily includes the costs of production. Operating income includes both COGS—or cost of sales—as well as operating expenses. However, operating income does not include items such as other income, non-operating income,?and non-operating expenses. Instead,?those figures are included in the net income calculation.

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