Edit Profile (opens in new tab) Micchelli, Charles A. Co-Author Distance Author ID: micchelli.charles-a Published as: Micchelli, Charles A.; Micchelli, C. A.; Micchelli, Charles; Micchelli, Ch. A.; Miccheli, Charles A.; Micchelli, C. A. E.; Micchelli, C. more...less External Links: MGP · dblp Documents Indexed: 279 Publications since 1972, including 4 Books 12 Contributions as Editor Co-Authors: 116 Co-Authors with 245 Joint Publications 3,486 Co-Co-Authors all top 5 Co-Authors 46 single-authored 49 Dahmen, Wolfgang A. 27 Xu, Yuesheng 18 Pinkus, Allan M. 17 Goodman, Timothy N. T. 13 Pontil, Massimiliano 11 Rivlin, Theodore Joseph 10 Cavaretta, Alfred S. jun. 9 Sharma, Ambikeshwar 8 Sauer, Tomas 7 Buhmann, Martin Dietrich 7 Chen, Zhongying 7 Dyn, Nira 6 Jia, Rong-Qing 6 Smith, Philip W. 5 Chen, Qiuhui 5 Fisher, Stephen D. 5 Gasca, Mariano 5 Mhaskar, Hrushikesh N. 4 Argyriou, Andreas 4 Karlin, Samuel 4 Lee, Yeon Ju 4 Prautzsch, Hartmut 4 Rodriguez, Giuseppe 4 Seatzu, Sebastiano 3 Basu, Sankar 3 Chen, Hanlin 3 Dinh Dũng 3 Edelman, Alan Stuart 3 Goldman, Ronald N. 3 Miranker, Willard Lee 3 Olsen, Peder A. 3 Shen, Lixin 3 Utreras, Florencio I. 3 Ward, Joseph Dinneen 3 Yoon, Jungho 3 Zhang, Haizhang 3 Zhou, Dingxuan 2 Barry, Phillip J. 2 DeVore, Ronald A. 2 Floater, Michael S. 2 Hoffman, Alan J. 2 Lawton, Wayne M. 2 Melkman, Avraham A. 2 Peña, Juan Manuel 2 Rinott, Yosef 2 Sun, Qiyu 2 Wang, Yi 2 Yu, Bo 1 Adler, Roy Lee 1 Baldassarre, Luca 1 Baxter, Brad J. C. 1 Boyd, Geoff 1 Caponnetto, Andrea 1 Carnicer, Jésus Miguel 1 Chui, Charles Kam-tai 1 Combettes, Patrick L. 1 Cotronei, Mariantonia 1 De Villiers, Johan Marthinus 1 Dikshit, Hanuman Prasad 1 Dress, Andreas W. M. 1 Evgeniou, Theodoros 1 Feig, Ephraim 1 FitzGerald, Carl H. 1 Friedland, Shmuel 1 Gal, Shmuel 1 Goh, Say Song 1 Gori, Laura 1 Gormaz, Raúl 1 Höllig, Klaus H. 1 Horváth, Gábor 1 Howard, Ralph E. 1 Hu, Rizhang 1 Hu, Yingsheng 1 Huy, Vu Nhat 1 Johnson, Olin G. 1 Khompurngson, Kannika 1 Kim, Hong Oh 1 Kitchens, Bruce P. 1 Lee, Seng Luan 1 Levin, David N. 1 Li, Chun 1 Li, Qia 1 Li, Xin 1 Li, Yuesheng 1 Li, Zheng 1 Limaye, Balmohan Vishnu 1 Liu, Jianqiang 1 Lo Cascio, Maria Laura 1 Mcdonald, Andrew M. 1 Milman, Pierre D. 1 Morales, Jean M. 1 Noakes, Lyle 1 Pai, Devidas V. 1 Paul, George 1 Peng, Silong 1 Rabut, Christophe 1 Ron, Amos 1 Said, Hassan B. 1 Schoenberg, Isaac Jacob 1 Seidel, Hans-Peter ...and 16 more Co-Authors all top 5 Serials 16 Advances in Computational Mathematics 13 Journal of Approximation Theory 9 Constructive Approximation 8 Numerische Mathematik 8 Numerical Algorithms 8 Linear Algebra and its Applications 7 Annals of Numerical Mathematics 6 SIAM Journal on Numerical Analysis 6 Computer Aided Geometric Design 6 Journal of Machine Learning Research (JMLR) 4 Mathematics of Computation 4 Journal of Computational and Applied Mathematics 4 Proceedings of the American Mathematical Society 4 Advances in Applied Mathematics 4 Journal of Complexity 4 Vietnam Journal of Mathematics 3 Journal of Mathematical Analysis and Applications 3 Transactions of the American Mathematical Society 3 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 3 SIAM Journal on Mathematical Analysis 3 Applied and Computational Harmonic Analysis 2 Inverse Problems 2 Israel Journal of Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Rocky Mountain Journal of Mathematics 2 Advances in Mathematics 2 Calcolo 2 Computing 2 Journal of Multivariate Analysis 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Results in Mathematics 2 Southeast Asian Bulletin of Mathematics 2 Analysis 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Approximation Theory and its Applications 2 SIAM Journal on Matrix Analysis and Applications 2 Aequationes Mathematicae 2 IBM Journal of Research and Development 2 RACSAM. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas 2 Analysis and Applications (Singapore) 2 Jaen Journal on Approximation 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 Journal d’Analyse Mathématique 1 Journal of the Australian Mathematical Society, Series B 1 Journal of the Institute of Mathematics and its Applications 1 Studia Mathematica 1 Arkiv för Matematik 1 American Journal of Mathematics 1 Applied Mathematics and Computation 1 BIT 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Indagationes Mathematicae 1 Indiana University Mathematics Journal 1 Journal of the Association for Computing Machinery 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Numerical Functional Analysis and Optimization 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Studia Scientiarum Mathematicarum Hungarica 1 Journal of Integral Equations 1 SIAM Journal on Scientific and Statistical Computing 1 Acta Mathematicae Applicatae Sinica. English Series 1 Multidimensional Systems and Signal Processing 1 Machine Learning 1 Neural Computation 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 The Journal of Fourier Analysis and Applications 1 East-West Journal of Mathematics 1 Communications on Pure and Applied Analysis 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Bulletin of the American Mathematical Society 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 ISNM. International Series of Numerical Mathematics 1 Lecture Notes in Pure and Applied Mathematics 1 Mathematics and its Applications (Dordrecht) 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 Series in Approximations and Decompositions 1 Cambridge Monographs on Applied and Computational Mathematics 1 NATO Science Series III: Computer & Systems Sciences 1 Complex Analysis and Operator Theory all top 5 Fields 165 Approximations and expansions (41-XX) 107 Numerical analysis (65-XX) 53 Harmonic analysis on Euclidean spaces (42-XX) 22 Computer science (68-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 14 Functions of a complex variable (30-XX) 14 Functional analysis (46-XX) 13 Statistics (62-XX) 11 General and overarching topics; collections (00-XX) 11 Operator theory (47-XX) 10 Integral equations (45-XX) 8 Combinatorics (05-XX) 8 Information and communication theory, circuits (94-XX) 6 Real functions (26-XX) 6 Differential geometry (53-XX) 6 Operations research, mathematical programming (90-XX) 6 Systems theory; control (93-XX) 5 Partial differential equations (35-XX) 5 Difference and functional equations (39-XX) 4 Number theory (11-XX) 4 Measure and integration (28-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geometry (51-XX) 3 Special functions (33-XX) 3 Convex and discrete geometry (52-XX) 3 Probability theory and stochastic processes (60-XX) 2 History and biography (01-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 General topology (54-XX) 2 Biology and other natural sciences (92-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Abstract harmonic analysis (43-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 246 Publications have been cited 4,925 times in 3,315 Documents Cited by ▼ Year ▼ Interpolation of scattered data: distance matrices and conditionally positive definite functions. Zbl 0625.41005 Micchelli, Charles A. 438 1986 Stationary subdivision. Zbl 0741.41009 Cavaretta, Alfred S.; Dahmen, Wolfgang; Micchelli, Charles A. 308 1991 Using the refinement equations for the construction of prewavelets. II: Powers of two. Zbl 0777.41013 Jia, Rong-Qing; Micchelli, Charles A. 150 1991 Some new characterizations of the Chebyshev polynomials. Zbl 0291.33012 Micchelli, C. A.; Rivlin, T. J. 106 1974 Proximity algorithms for image models: denoising. Zbl 1216.94015 Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 96 2011 Universal kernels. Zbl 1222.68266 Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 88 2006 A survey of optimal recovery. Zbl 0386.93045 Micchelli, C. A.; Rivlin, T. J. 84 1978 Uniform refinement of curves. Zbl 0668.65011 Micchelli, Charles A.; Prautzsch, Hartmut 83 1989 Translates of multivariate splines. Zbl 0522.41009 Dahmen, Wolfgang; Micchelli, Charles A. 82 1983 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015 Mhaskar, H. N.; Micchelli, Charles A. 80 1992 A constructive approach to Kergin interpolation in \(R^ k\): Multivariate B-splines and Lagrange interpolation. Zbl 0456.41003 Micchelli, Charles A. 72 1980 Learning the kernel function via regularization. Zbl 1222.68265 Micchelli, Charles A.; Pontil, Massimiliano 68 2005 On learning vector-valued functions. Zbl 1092.93045 Micchelli, Charles A.; Pontil, Massimiliano 64 2005 Optimal nonlinear approximation. Zbl 0682.41033 De Vore, Ronald A.; Howard, Ralph; Micchelli, Charles 60 1989 Using the refinement equation for evaluating integrals of wavelets. Zbl 0773.65006 Dahmen, Wolfgang; Micchelli, Charles A. 59 1993 Using the matrix refinement equation for the construction of wavelets on invariant sets. Zbl 0815.42019 Micchelli, Charles A.; Xu, Yuesheng 57 1994 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012 Mhaskar, H. N.; Micchelli, Charles A. 57 1995 Fast collocation methods for second kind integral equations. Zbl 1016.65107 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 53 2002 Optimal estimation of linear operators in Hilbert spaces from inaccurate data. Zbl 0399.65037 Melkman, Avraham A.; Micchelli, Charles A. 53 1979 Polynomial preconditioners for conjugate gradient calculations. Zbl 0563.65020 Johnson, Olin G.; Micchelli, Charles A.; Paul, George 52 1983 Learning multiple tasks with kernel methods. Zbl 1222.68197 Evgeniou, Theodoros; Micchelli, Charles A.; Pontil, Massimiliano 52 2005 On linear independence for integer translates of a finite number of functions. Zbl 0790.41016 Jia, Rong-Qing; Micchelli, Charles A. 51 1993 Biorthogonal wavelet expansions. Zbl 0882.65148 Dahmen, W.; Micchelli, C. A. 50 1997 Recent progress in multivariate splines. Zbl 0559.41011 Dahmen, Wolfgang; Micchelli, Charles A. 49 1983 On the local linear independence of translates of a box spline. Zbl 0545.41018 Dahmen, Wolfgang; Micchelli, Charles A. 49 1985 Spectral radius formulas for subdivision operators. Zbl 0840.42020 Goodman, T. N. T.; Micchelli, Charles A.; Ward, J. D. 48 1994 The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes. Zbl 0915.65134 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 44 1997 Reconstruction and decomposition algorithms for biorthogonal multiwavelets. Zbl 0872.42010 Micchelli, Charles A.; Xu, Yuesheng 44 1997 Total positivity and its applications. Meeting, Zaragoza in Jaca, Spain, September 26–30, 1994. Zbl 0884.00045 42 1996 The n-width of sets of analytic functions. Zbl 0451.30032 Fisher, S. D.; Micchelli, Charles A. 41 1980 Lectures on optimal recovery. Zbl 0698.41024 Micchelli, C. A.; Rivlin, T. J. 40 1984 Constrained \(L_ p\) approximation. Zbl 0582.41002 Micchelli, C. A.; Smith, P. W.; Swetits, J.; Ward, J. D. 39 1985 On vector subdivision. Zbl 0930.65007 Micchelli, Charles A.; Sauer, Thomas 38 1998 Regularity of multiwavelets. Zbl 0902.65095 Micchelli, C. A.; Sauer, Thomas 38 1997 Wavelet Galerkin methods for second-kind integral equations. Zbl 0913.65129 Micchelli, Charles A.; Xu, Yuesheng; Zhao, Yunhe 38 1997 A multilevel method for solving operator equations. Zbl 0990.65059 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 37 2001 On the solution of certain systems of partial difference equations and linear dependence of translates of box splines. Zbl 0637.41012 Dahmen, Wolfgang; Micchelli, Charles A. 37 1985 A construction of interpolating wavelets on invariant sets. Zbl 1051.65009 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 1999 Multiscale methods for Fredholm integral equations. Zbl 1332.65188 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 2015 Piecewise polynomial spaces and geometric continuity of curves. Zbl 0638.65010 Dyn, Nira; Micchelli, Charles A. 36 1988 Smoothing and interpolation in a convex subset of a Hilbert space. Zbl 0651.65046 Micchelli, Charles A.; Utreras, Florencio I. 36 1988 Moment theory for weak Chebyshev systems with applications to monosplines, quadrature formulae and best one-sided \(L^1\)-approximation by spline functions with fixed knots. Zbl 0353.41003 Micchelli, C. A.; Pinkus, Allan 35 1977 The optimal recovery of smooth functions. Zbl 0335.65004 Micchelli, C. A.; Rivlin, T. J.; Winograd, S. 34 1976 Universal multi-task kernels. Zbl 1225.68155 Caponnetto, Andrea; Micchelli, Charles A.; Pontil, Massimiliano; Ying, Yiming 34 2008 The saturation class and iterates of the Bernstein polynomials. Zbl 0258.41012 Micchelli, Charles 32 1973 Interpolatory subdivision schemes and wavelets. Zbl 0883.42024 Micchelli, Charles A. 32 1996 Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014 Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying 32 2013 Compactly supported fundamental functions for spline interpolation. Zbl 0646.65012 Dahmen, Wolfgang; Goodman, T. N. T.; Micchelli, Charles A. 31 1988 Using the refinement equation for the construction of pre-wavelets. Zbl 0759.65005 Micchelli, Charles A. 31 1991 Some problems in the approximation of functions of two variables and n- widths of integral operators. Zbl 0396.41014 Micchelli, Charles A.; Pinkus, Allan 29 1978 Mathematical aspects of geometric modeling. Zbl 0864.65008 Micchelli, Charles A. 29 1995 The number of solutions to linear diophantine equations and multivariate splines. Zbl 0655.10013 Dahmen, Wolfgang; Micchelli, Charles A. 29 1988 Blossoming begets \(B\)-spline bases built better by \(B\)-patches. Zbl 0757.41014 Dahmen, Wolfgang; Micchelli, Charles A.; Seidel, Hans-Peter 29 1992 Subdivision algorithms for the generation of box spline surfaces. Zbl 0581.65011 Dahmen, Wolfgang; Micchelli, Charles A. 28 1984 On multivariate E-splines. Zbl 0706.41010 Dahmen, Wolfgang; Micchelli, Charles A. 28 1989 Spectral fractorization of Laurent polynomials. Zbl 0886.65013 Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 28 1997 Convexity of multivariate Bernstein polynomials and box spline surfaces. Zbl 0689.41013 Dahmen, Wolfgang; Micchelli, Charles A. 27 1988 The fundamental theorem of algebra for monosplines satisfying boundary conditions. Zbl 0294.41016 Karlin, Samuel; Micchelli, Charles 26 1972 Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 26 2002 On a numerically efficient method for computing multivariate B-splines. Zbl 0422.41008 Micchelli, Charles A. 24 1979 Nonlinear stationary subdivision. Zbl 0902.41001 Floater, Michael S.; Micchelli, Charles A. 24 1998 Almost strictly totally positive matrices. Zbl 0752.15016 Gasca, M.; Micchelli, Charles A.; Peña, J. M. 24 1992 Studies in spline functions and approximation theory. Zbl 0323.00007 Karlin, Samuel; Micchelli, Charles A.; Pinkus, Allan; Schoenberg, I. J. 23 1976 Best \(L^1\) approximation by weak Chebyshev systems and the uniqueness of interpolating perfect splines. Zbl 0339.41022 Micchelli, Charles A. 23 1977 Multivariate splines: a probabilistic perspective. Zbl 0623.41014 Karlin, S.; Micchelli, C. A.; Rinott, Y. 23 1986 On refinement equations determined by Pólya frequency sequences. Zbl 0761.42015 Goodman, T. N. T.; Micchelli, Charles A. 23 1992 A formula for Kergin interpolation in \(R^ k\). Zbl 0454.41002 Micchelli, Charles A.; Milman, Pierre 22 1980 Turan formulae and highest precision quadrature rules for Chebyshev coefficients. Zbl 0288.65013 Micchelli, C. A.; Rivlin, T. J. 22 1972 A function representation for learning in Banach spaces. Zbl 1078.68129 Micchelli, Charles A.; Pontil, Massimiliano 22 2004 On the approximation order from certain multivariate spline spaces. Zbl 0558.41013 Dahmen, Wolfgang; Micchelli, Charles A. 22 1984 Multiquadratic interpolation improved. Zbl 0764.41001 Buhmann, Martin D.; Micchelli, Charles A. 22 1992 On the linear independence of multivariate B-splines. I. Triangulations of simploids. Zbl 0498.41004 Dahmen, Wolfgang A.; Micchelli, Charles A. 21 1982 A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085 Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 21 2012 On functions which preserve the class of Stieltjes matrices. Zbl 0405.15011 Micchelli, Charles A.; Willoughby, R. A. 20 1979 Using the refinement equation for the construction of pre-wavelets. V: Extensibility of trigonometric polynomials. Zbl 0765.65023 Jia, R.-Q.; Micchelli, C. A. 20 1992 When is there a representer theorem? Vector versus matrix regularizers. Zbl 1235.68128 Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 20 2009 On spectral learning. Zbl 1242.68201 Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 20 2010 Optimal sequential and non-sequential procedures for evaluating a functional. Zbl 0445.65010 Gal, Shmuel; Micchelli, Charles A. 19 1980 Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Zbl 0558.41012 Micchelli, Charles A. 19 1984 Spline spaces are optimal for \(L^2\) n-width. Zbl 0384.41005 Melkman, Avraham A.; Micchelli, Charles A. 18 1978 Cardinal \(\mathcal L\)-splines. Zbl 0343.41008 Micchelli, Charles A. 17 1976 Weak convergence of the area of nonparametric \(L_1\) surfaces. Zbl 0412.41018 Micchelli, Ch. A.; Pinkus, A. 16 1977 Quadrature formulae and Hermite-Birkhoff interpolation. Zbl 0259.41016 Micchelli, C. A.; Rivlin, T. J. 16 1973 On weight functions which admit explicit Gauss-Turán quadrature formulas. Zbl 0853.65027 Gori, Laura; Micchelli, Charles A. 16 1996 Corner cutting algorithms for the Bézier representation of free form curves. Zbl 0652.41003 Goodman, T. N. T.; Micchelli, Charles A. 16 1988 Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces. Zbl 0784.15005 Dahmen, Wolfgang; Micchelli, Charles A. 16 1993 Using parameters to increase smoothness of curves and surfaces generated by subdivision. Zbl 0711.65007 Dyn, Nira; Levin, David; Micchelli, Charles A. 15 1990 Admissible slopes for monotone and convex interpolation. Zbl 0624.41001 Edelman, Alan; Micchelli, Charles A. 15 1987 Functions that preserve families of positive semidefinite matrices. Zbl 0852.43004 FitzGerald, Carl H.; Micchelli, Charles A.; Pinkus, Allan 15 1995 Using the refinement equation for the construction of pre-wavelets. III: Elliptic splines. Zbl 0765.65024 Micchelli, Charles A.; Rabut, Christophe; Utreras, Florencio I. 15 1991 Chebyshev subspaces and convergence of positive linear operators. Zbl 0268.41008 Micchelli, C. A. 14 1973 Convergence of positive linear operators on C(X). Zbl 0294.41032 Micchelli, C. A. 14 1975 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012 Mhaskar, H. N.; Micchelli, C. A. 14 1994 Continuous refinement equations and subdivision. Zbl 0824.65144 Dahmen, Wolfgang; Micchelli, Charles A. 14 1993 Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182 Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 14 2009 Numerical integration rules near Gaussian quadrature. Zbl 0287.65014 Micchelli, C. A.; Rivlin, T. J. 13 1974 Error bounds for learning the kernel. Zbl 1392.68357 Micchelli, Charles A.; Pontil, Massimiliano; Wu, Qiang; Zhou, Ding-Xuan 13 2016 Uncertainty principles in Hilbert spaces. Zbl 1027.47028 Goh, Say Song; Micchelli, Charles A. 13 2002 Approximation by radial bases and neural networks. Zbl 0976.65014 Li, Xin; Micchelli, Charles A. 13 2000 Statistical encounters with B-splines. Zbl 0615.62021 Dahmen, Wolfgang; Micchelli, Charles A. 13 1986 Fixed-point proximity algorithm for minimal norm interpolation. Zbl 1440.15015 Li, Zheng; Micchelli, Charles A.; Xu, Yuesheng 3 2020 Approximation by translates of a single function of functions in space induced by the convolution with a given function. Zbl 1428.41040 Dũng, Dinh; Micchelli, Charles A.; Huy, Vu Nhat 1 2019 Error bounds for learning the kernel. Zbl 1392.68357 Micchelli, Charles A.; Pontil, Massimiliano; Wu, Qiang; Zhou, Ding-Xuan 13 2016 Corrigendum to “Multivariate approximation by translates of the Korobov function on Smolyak grids”. Zbl 1382.42005 Dũng, Dinh; Micchelli, Charles A. 2 2016 On multivariate discrete least squares. Zbl 1358.41005 Lee, Yeon Ju; Micchelli, Charles A.; Yoon, Jungho 1 2016 Multiscale methods for Fredholm integral equations. Zbl 1332.65188 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 2015 A study on multivariate interpolation by increasingly flat kernel functions. Zbl 1331.41003 Lee, Yeon Ju; Micchelli, Charles A.; Yoon, Jungho 5 2015 On convergence of flat multivariate interpolation by translation kernels with finite smoothness. Zbl 1308.41001 Lee, Yeon Ju; Micchelli, Charles A.; Yoon, Jungho 9 2014 Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014 Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying 32 2013 Regularizers for structured sparsity. Zbl 1297.62153 Micchelli, Charles A.; Morales, Jean M.; Pontil, Massimiliano 11 2013 Multivariate approximation by translates of the Korobov function on Smolyak grids. Zbl 1305.42006 Dũng, Dinh; Micchelli, Charles A. 5 2013 On computing with the Hilbert spline transform. Zbl 1268.41005 Micchelli, Charles A.; Xu, Yuesheng; Yu, Bo 4 2013 On collocation matrices for interpolation and approximation. Zbl 1282.41002 Lee, Yeon Ju; Micchelli, Charles A. 3 2013 Finite rank kernels for multi-task learning. Zbl 1267.41003 Liu, Jianqiang; Micchelli, Charles A.; Wang, Rui; Xu, Yuesheng 2 2013 On sparsity inducing regularization methods for machine learning. Zbl 1330.68245 Argyriou, Andreas; Baldassarre, Luca; Micchelli, Charles A.; Pontil, Massimiliano 1 2013 A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085 Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 21 2012 The Bedrosian identity for functions analytic in a neighborhood of the unit circle. Zbl 1276.42008 Chen, Qiuhui; Micchelli, Charles A. 4 2012 Proximity algorithms for image models: denoising. Zbl 1216.94015 Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 96 2011 Hide. Zbl 1263.46028 Khompurngson, Kannika; Micchelli, Charles A. 1 2011 On spectral learning. Zbl 1242.68201 Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 20 2010 Functions with spline spectra and their applications. Zbl 1186.42014 Chen, Qiuhui; Micchelli, Charles A.; Wang, Yi 7 2010 When is there a representer theorem? Vector versus matrix regularizers. Zbl 1235.68128 Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 20 2009 Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182 Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 14 2009 Universal multi-task kernels. Zbl 1225.68155 Caponnetto, Andrea; Micchelli, Charles A.; Pontil, Massimiliano; Ying, Yiming 34 2008 On translation invariant operators which preserve the B-spline recurrence. Zbl 1283.41010 Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 1 2008 Feature space perspectives for learning the kernel. Zbl 1470.68148 Micchelli, Charles A.; Pontil, Massimiliano 6 2007 Interpolation filters with prescribed zeros and their refinable functions. Zbl 1214.42074 Micchelli, C. A.; Sun, Q. 2 2007 On the matrix completion problem for multivariate filter bank construction. Zbl 1128.65111 Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng 2 2007 Universal kernels. Zbl 1222.68266 Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 88 2006 Refinable functions from Blaschke products. Zbl 1134.42337 Cotronei, Mariantonia; Lo Cascio, Maria Laura; Kim, Hong Oh; Micchelli, Charles A.; Sauer, Tomas 3 2006 Learning the kernel function via regularization. Zbl 1222.68265 Micchelli, Charles A.; Pontil, Massimiliano 68 2005 On learning vector-valued functions. Zbl 1092.93045 Micchelli, Charles A.; Pontil, Massimiliano 64 2005 Learning multiple tasks with kernel methods. Zbl 1222.68197 Evgeniou, Theodoros; Micchelli, Charles A.; Pontil, Massimiliano 52 2005 Learning convex combinations of continuously parameterized basic kernels. Zbl 1137.68517 Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 10 2005 Biorthogonal multivariate filter banks from centrally symmetric matrices. Zbl 1079.65141 Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng 1 2005 Rao distances. Zbl 1116.62354 Micchelli, Charles A.; Noakes, Lyle 1 2005 A function representation for learning in Banach spaces. Zbl 1078.68129 Micchelli, Charles A.; Pontil, Massimiliano 22 2004 Selected papers of Alan J. Hoffman. With commentary. Edited by Charles A. Micchelli. Zbl 1041.01013 Hoffman, Alan J. 13 2003 Multivariate filter banks having matrix factorizations. Zbl 1043.42026 Chen, Qiuhui; Micchelli, Charles A.; Peng, Silong; Xu, Yuesheng 7 2003 Advances in learning theory. Methods, models and applications. Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, July 8–19, 2002. Zbl 1079.68601 Basu, S. 1 2003 Refinable functions: positivity and interpolation. Zbl 1071.42025 Micchelli, Charles A.; Zhou, Ding-Xuan 1 2003 Continuous refinable functions and self similarity. Zbl 1087.42026 Micchelli, Charles A.; Sauer, Thomas 1 2003 Fast collocation methods for second kind integral equations. Zbl 1016.65107 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 53 2002 Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 26 2002 Uncertainty principles in Hilbert spaces. Zbl 1027.47028 Goh, Say Song; Micchelli, Charles A. 13 2002 Refinable functions from their values at integers. Zbl 1035.42036 Micchelli, Charles A.; Sun, Qiyu 1 2002 A multilevel method for solving operator equations. Zbl 0990.65059 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 37 2001 Subdivision schemes for iterated function systems. Zbl 0978.54012 Micchelli, Charles A.; Sauer, Thomas; Xu, Yuesheng 4 2001 Riesz bases in subspaces of \(L_2 (\mathbb{R}_+)\). Zbl 0997.46024 Goodman, T. N. T.; Micchelli, C. A.; Shen, Zuowei 3 2001 Binomial matrices. Zbl 0996.15005 Boyd, Geoff; Micchelli, Charles A.; Strang, Gilbert; Zhou, Ding-Xuan 1 2001 Approximation by radial bases and neural networks. Zbl 0976.65014 Li, Xin; Micchelli, Charles A. 13 2000 On the Cholesky factorization of the Gram matrix of multivariate functions. Zbl 0977.65024 Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 10 2000 Building refinable functions from their values at integers. Zbl 0971.65123 de Villiers, Johan M.; Micchelli, Charles A.; Sauer, Thomas 4 2000 Bézout identities with inequality constraints. Zbl 0971.65124 Lawton, Wayne M.; Micchelli, Charles A. 3 2000 Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic data. Zbl 0962.65008 Micchelli, Charles A.; Olsen, Peder 2 2000 A construction of interpolating wavelets on invariant sets. Zbl 1051.65009 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 1999 On vector subdivision. Zbl 0930.65007 Micchelli, Charles A.; Sauer, Thomas 38 1998 Nonlinear stationary subdivision. Zbl 0902.41001 Floater, Michael S.; Micchelli, Charles A. 24 1998 A construction of refinable sets for interpolating wavelets. Zbl 0921.65097 Micchelli, Charles A.; Sauer, Thomas; Xu, Yuesheng 8 1998 On the spectral radius of a bi-infinite periodic and slanted matrix. Zbl 0920.15002 Goodman, Tim N. T.; Jia, Rong-Qing; Micchelli, Charles A. 7 1998 On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions. Zbl 0909.65006 Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 5 1998 Biorthogonal wavelet expansions. Zbl 0882.65148 Dahmen, W.; Micchelli, C. A. 50 1997 The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes. Zbl 0915.65134 Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 44 1997 Reconstruction and decomposition algorithms for biorthogonal multiwavelets. Zbl 0872.42010 Micchelli, Charles A.; Xu, Yuesheng 44 1997 Regularity of multiwavelets. Zbl 0902.65095 Micchelli, C. A.; Sauer, Thomas 38 1997 Wavelet Galerkin methods for second-kind integral equations. Zbl 0913.65129 Micchelli, Charles A.; Xu, Yuesheng; Zhao, Yunhe 38 1997 Spectral fractorization of Laurent polynomials. Zbl 0886.65013 Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 28 1997 Sobolev norm convergence of stationary subdivision schemes. Zbl 0937.65148 Micchelli, Charles A.; Sauer, Thomas 5 1997 Construction of conjugate quadrature filters with specified zeros. Zbl 0902.65008 Lawton, Wayne; Micchelli, Charles A. 4 1997 On a family of filters arising in wavelet construction. Zbl 0866.42026 Micchelli, Charles A. 4 1997 On a measure of dissimilarity for normal probability densities. Zbl 1090.62541 Micchelli, Charles A. 1 1997 Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024 Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos 1 1997 Total positivity and its applications. Meeting, Zaragoza in Jaca, Spain, September 26–30, 1994. Zbl 0884.00045 42 1996 Interpolatory subdivision schemes and wavelets. Zbl 0883.42024 Micchelli, Charles A. 32 1996 On weight functions which admit explicit Gauss-Turán quadrature formulas. Zbl 0853.65027 Gori, Laura; Micchelli, Charles A. 16 1996 On multivariate splines, matroids, and the ext-functor. Zbl 0908.41004 Dahmen, Wolfgang; Dress, Andreas; Micchelli, Charles A. 3 1996 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012 Mhaskar, H. N.; Micchelli, Charles A. 57 1995 Mathematical aspects of geometric modeling. Zbl 0864.65008 Micchelli, Charles A. 29 1995 Functions that preserve families of positive semidefinite matrices. Zbl 0852.43004 FitzGerald, Carl H.; Micchelli, Charles A.; Pinkus, Allan 15 1995 On the Cholesky factorization of the Gram matrix of locally supported functions. Zbl 0833.15010 Goodman, T. N. T.; Micchelli, C. A.; Rodriguez, G.; Seatzu, S. 7 1995 Spectral radius formulas for the dilation-convolution integral operator. Zbl 0843.42014 Goodman, T. N. T.; Micchelli, Charles; Ward, J. D. 3 1995 Weakly singular Fredholm integral equations. I: Singularity preserving wavelet-Galerkin methods. Zbl 0928.65165 Micchelli, Charles A.; Xu, Yuesheng 2 1995 Using the matrix refinement equation for the construction of wavelets on invariant sets. Zbl 0815.42019 Micchelli, Charles A.; Xu, Yuesheng 57 1994 Spectral radius formulas for subdivision operators. Zbl 0840.42020 Goodman, T. N. T.; Micchelli, Charles A.; Ward, J. D. 48 1994 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012 Mhaskar, H. N.; Micchelli, C. A. 14 1994 Using two-slanted matrices for subdivision. Zbl 0802.65003 Buhmann, Martin D.; Micchelli, Charles A. 8 1994 Orthonormal cardinal functions. Zbl 0857.42021 Goodman, T. N. T.; Micchelli, Charles A. 6 1994 Variational problems arising from balancing several error criteria. Zbl 0809.49021 Micchelli, C. A.; Pinkus, A. 4 1994 Banded matrices with banded inverses. III: p-slanted matrices. Zbl 0817.65032 Gasca, M.; Micchelli, C. A.; Peña, J. M. 3 1994 Norm estimates for the \(l^ 2\)-inverses of multivariate Toeplitz matrices. Zbl 0790.15024 Baxter, B. J. C.; Micchelli, C. A. E. 2 1994 Using the matrix refinement equation for the construction of wavelets. II: Smooth wavelets on \([0,1]\). Zbl 0888.42021 Micchelli, Charles A.; Xu, Yuesheng 2 1994 Using the refinement equation for evaluating integrals of wavelets. Zbl 0773.65006 Dahmen, Wolfgang; Micchelli, Charles A. 59 1993 On linear independence for integer translates of a finite number of functions. Zbl 0790.41016 Jia, Rong-Qing; Micchelli, Charles A. 51 1993 Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces. Zbl 0784.15005 Dahmen, Wolfgang; Micchelli, Charles A. 16 1993 Continuous refinement equations and subdivision. Zbl 0824.65144 Dahmen, Wolfgang; Micchelli, Charles A. 14 1993 Optimal estimation of linear operators from inaccurate data: A second look. Zbl 0794.65052 Micchelli, Charles A. 6 1993 Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices. Zbl 0824.65005 Barry, Phillip J.; Goldman, Ronald N.; Micchelli, Charles A. 6 1993 Using the refinement equation for the construction of pre-wavelets. IV: Cube splines and elliptic splines united. Zbl 0784.65012 Micchelli, Charles A. 1 1993 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015 Mhaskar, H. N.; Micchelli, Charles A. 80 1992 Blossoming begets \(B\)-spline bases built better by \(B\)-patches. Zbl 0757.41014 Dahmen, Wolfgang; Micchelli, Charles A.; Seidel, Hans-Peter 29 1992 ...and 146 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,595 Authors 92 Micchelli, Charles A. 58 Xu, Yuesheng 41 Jia, Rong-Qing 39 Dahmen, Wolfgang A. 37 Dyn, Nira 33 Peña, Juan Manuel 32 Conti, Costanza 32 Goodman, Timothy N. T. 30 Sauer, Tomas 29 Chui, Charles Kam-tai 26 Amat Plata, Sergio 26 Ron, Amos 23 Osipenko, Konstantin Yur’evich 23 Shen, Lixin 23 Sun, Qiyu 23 Yoon, Jungho 22 Pinkus, Allan M. 22 Shen, Zuowei 21 Romani, Lucia 20 Lee, Seng Luan 20 Zhou, Dingxuan 18 Levin, David N. 18 Li, Song 18 Zhang, Haizhang 17 Charina, Maria 17 Chen, Zhongying 17 DeVore, Ronald A. 17 Ward, Joseph Dinneen 15 Buhmann, Martin Dietrich 15 Cao, Feilong 15 Carnicer, Jésus Miguel 15 de Boor, Carl 15 Manni, Carla 15 Mazure, Marie-Laurence 15 Mhaskar, Hrushikesh N. 15 Spalević, Miodrag M. 14 Chen, Dirong 14 Han, Bin 14 Power, Henry 13 Avazzadeh, Zakieh 13 Cohen, Albert 13 Floater, Michael S. 13 Kansa, Edward J. 13 Nikan, Omid 12 Boyanov, Borislav Dechev 12 Haq, Sirajul 12 Jetter, Kurt 12 Long, Guangqing 12 Prautzsch, Hartmut 12 Sharma, Ambikeshwar 12 Sheng, Baohuai 12 Trillo, Juan Carlos 12 Zhou, Xinlong 11 Cotronei, Mariantonia 11 Goh, Say Song 11 Goldman, Ronald N. 11 Hon, Yiu-Chung 11 Jiang, Qingtang 11 Lee, Yeon Ju 11 Liandrat, Jacques 11 Lu, Jian 11 Lyche, Tom 11 Milovanović, Gradimir V. 11 Nelakanti, Gnaneshwar 11 Petrova, Guergana 11 Protasov, Vladimir Yu. 11 San Antolín, Angel 11 Speleers, Hendrik 11 Tang, Yuchao 11 Unser, Michael A. 11 Vergne, Michèle 11 Wang, Rui 11 Wasilkowski, Grzegorz W. 10 Barrera, Domingo 10 Barton, Michael H. 10 De Villiers, Johan Marthinus 10 Gori, Laura 10 Jiang, Ying 9 Beccari, Carolina Vittoria 9 Casciola, Giulio 9 Costarelli, Danilo 9 Dahlke, Stephan 9 Daubechies, Ingrid Chantal 9 Guillot, Dominique 9 Khare, Apoorva 9 Li, Xin 9 Magaril-Il’yaev, Gregoriĭ Geogrievich 9 Mathé, Peter 9 Merrien, Jean-Louis 9 Pereverzev, Sergei V. 9 Pitolli, Francesca 9 Plaskota, Leszek 9 Plonka, Gerlind 9 Sablonnière, Paul 9 Schaback, Robert 9 Uddin, Marjan 9 Wang, Renhong 9 Woźniakowski, Henryk 9 Yang, Hongqi 8 Alonso, Pedro ...and 3,495 more Authors all top 5 Cited in 434 Serials 273 Journal of Approximation Theory 176 Journal of Computational and Applied Mathematics 121 Advances in Computational Mathematics 105 Computer Aided Geometric Design 104 Applied and Computational Harmonic Analysis 93 Applied Mathematics and Computation 85 Linear Algebra and its Applications 84 Computers & Mathematics with Applications 84 Constructive Approximation 74 Journal of Mathematical Analysis and Applications 73 Journal of Complexity 63 Engineering Analysis with Boundary Elements 59 Mathematics of Computation 58 Numerical Algorithms 42 Applied Numerical Mathematics 38 Numerische Mathematik 38 Proceedings of the American Mathematical Society 36 Computer Methods in Applied Mechanics and Engineering 35 Transactions of the American Mathematical Society 33 Journal of Computational Physics 32 International Journal of Wavelets, Multiresolution and Information Processing 31 Mathematical Notes 31 BIT 31 Numerical Functional Analysis and Optimization 30 Journal of Scientific Computing 29 Machine Learning 28 International Journal of Computer Mathematics 27 Neural Networks 27 The Journal of Fourier Analysis and Applications 25 Acta Mathematica Sinica. 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