Edit Profile (opens in new tab) Micchelli, Charles A. Compute Distance To: Compute 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: 113 Co-Authors with 244 Joint Publications 3,479 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 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 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 1 Shen, Zuowei 1 Strang, William Gilbert 1 Suykens, Johan A. K. ...and 13 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 Cambridge Monographs on Applied and Computational Mathematics 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 241 Publications have been cited 4,502 times in 3,019 Documents Cited by ▼ Year ▼ Interpolation of scattered data: distance matrices and conditionally positive definite functions. Zbl 0625.41005Micchelli, Charles A. 407 1986 Stationary subdivision. Zbl 0741.41009Cavaretta, Alfred S.; Dahmen, Wolfgang; Micchelli, Charles A. 292 1991 Using the refinement equations for the construction of prewavelets. II: Powers of two. Zbl 0777.41013Jia, Rong-Qing; Micchelli, Charles A. 132 1991 Some new characterizations of the Chebyshev polynomials. Zbl 0291.33012Micchelli, C. A.; Rivlin, T. J. 99 1974 Uniform refinement of curves. Zbl 0668.65011Micchelli, Charles A.; Prautzsch, Hartmut 81 1989 Translates of multivariate splines. Zbl 0522.41009Dahmen, Wolfgang; Micchelli, Charles A. 80 1983 Proximity algorithms for image models: denoising. Zbl 1216.94015Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 79 2011 Universal kernels. Zbl 1222.68266Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 75 2006 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015Mhaskar, H. N.; Micchelli, Charles A. 74 1992 A constructive approach to Kergin interpolation in \(R^ k\): Multivariate B-splines and Lagrange interpolation. Zbl 0456.41003Micchelli, Charles A. 70 1980 Learning the kernel function via regularization. Zbl 1222.68265Micchelli, Charles A.; Pontil, Massimiliano 64 2005 A survey of optimal recovery. Zbl 0386.93045Micchelli, C. A.; Rivlin, T. J. 64 1978 Using the refinement equation for evaluating integrals of wavelets. Zbl 0773.65006Dahmen, Wolfgang; Micchelli, Charles A. 58 1993 On learning vector-valued functions. Zbl 1092.93045Micchelli, Charles A.; Pontil, Massimiliano 54 2005 Fast collocation methods for second kind integral equations. Zbl 1016.65107Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 52 2002 Using the matrix refinement equation for the construction of wavelets on invariant sets. Zbl 0815.42019Micchelli, Charles A.; Xu, Yuesheng 51 1994 Polynomial preconditioners for conjugate gradient calculations. Zbl 0563.65020Johnson, Olin G.; Micchelli, Charles A.; Paul, George 51 1983 Biorthogonal wavelet expansions. Zbl 0882.65148Dahmen, W.; Micchelli, C. A. 50 1997 On linear independence for integer translates of a finite number of functions. Zbl 0790.41016Jia, Rong-Qing; Micchelli, Charles A. 49 1993 On the local linear independence of translates of a box spline. Zbl 0545.41018Dahmen, Wolfgang; Micchelli, Charles A. 49 1985 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012Mhaskar, H. N.; Micchelli, Charles A. 49 1995 Optimal estimation of linear operators in Hilbert spaces from inaccurate data. Zbl 0399.65037Melkman, Avraham A.; Micchelli, Charles A. 48 1979 Learning multiple tasks with kernel methods. Zbl 1222.68197Evgeniou, Theodoros; Micchelli, Charles A.; Pontil, Massimiliano 47 2005 Spectral radius formulas for subdivision operators. Zbl 0840.42020Goodman, T. N. T.; Micchelli, Charles A.; Ward, J. D. 46 1994 Optimal nonlinear approximation. Zbl 0682.41033De Vore, Ronald A.; Howard, Ralph; Micchelli, Charles 44 1989 The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes. Zbl 0915.65134Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 43 1997 The n-width of sets of analytic functions. Zbl 0451.30032Fisher, S. D.; Micchelli, Charles A. 40 1980 Constrained \(L_ p\) approximation. Zbl 0582.41002Micchelli, C. A.; Smith, P. W.; Swetits, J.; Ward, J. D. 38 1985 Recent progress in multivariate splines. Zbl 0559.41011Dahmen, Wolfgang; Micchelli, Charles A. 38 1983 Reconstruction and decomposition algorithms for biorthogonal multiwavelets. Zbl 0872.42010Micchelli, Charles A.; Xu, Yuesheng 38 1997 Regularity of multiwavelets. Zbl 0902.65095Micchelli, C. A.; Sauer, Thomas 37 1997 Piecewise polynomial spaces and geometric continuity of curves. Zbl 0638.65010Dyn, Nira; Micchelli, Charles A. 36 1988 Smoothing and interpolation in a convex subset of a Hilbert space. Zbl 0651.65046Micchelli, Charles A.; Utreras, Florencio I. 36 1988 A multilevel method for solving operator equations. Zbl 0990.65059Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 2001 Wavelet Galerkin methods for second-kind integral equations. Zbl 0913.65129Micchelli, Charles A.; Xu, Yuesheng; Zhao, Yunhe 36 1997 On the solution of certain systems of partial difference equations and linear dependence of translates of box splines. Zbl 0637.41012Dahmen, Wolfgang; Micchelli, Charles A. 35 1985 On vector subdivision. Zbl 0930.65007Micchelli, Charles A.; Sauer, Thomas 35 1998 The optimal recovery of smooth functions. Zbl 0335.65004Micchelli, C. A.; Rivlin, T. J.; Winograd, S. 35 1976 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 0353.41003Micchelli, C. A.; Pinkus, Allan 34 1977 A construction of interpolating wavelets on invariant sets. Zbl 1051.65009Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 33 1999 Universal multi-task kernels. Zbl 1225.68155Caponnetto, Andrea; Micchelli, Charles A.; Pontil, Massimiliano; Ying, Yiming 33 2008 Interpolatory subdivision schemes and wavelets. Zbl 0883.42024Micchelli, Charles A. 32 1996 Lectures on optimal recovery. Zbl 0698.41024Micchelli, C. A.; Rivlin, T. J. 32 1984 Using the refinement equation for the construction of pre-wavelets. Zbl 0759.65005Micchelli, Charles A. 31 1991 Compactly supported fundamental functions for spline interpolation. Zbl 0646.65012Dahmen, Wolfgang; Goodman, T. N. T.; Micchelli, Charles A. 31 1988 The saturation class and iterates of the Bernstein polynomials. Zbl 0258.41012Micchelli, Charles 29 1973 Blossoming begets \(B\)-spline bases built better by \(B\)-patches. Zbl 0757.41014Dahmen, Wolfgang; Micchelli, Charles A.; Seidel, Hans-Peter 28 1992 On multivariate E-splines. Zbl 0706.41010Dahmen, Wolfgang; Micchelli, Charles A. 28 1989 The number of solutions to linear diophantine equations and multivariate splines. Zbl 0655.10013Dahmen, Wolfgang; Micchelli, Charles A. 28 1988 Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying 28 2013 Some problems in the approximation of functions of two variables and n- widths of integral operators. Zbl 0396.41014Micchelli, Charles A.; Pinkus, Allan 28 1978 Convexity of multivariate Bernstein polynomials and box spline surfaces. Zbl 0689.41013Dahmen, Wolfgang; Micchelli, Charles A. 27 1988 Subdivision algorithms for the generation of box spline surfaces. Zbl 0581.65011Dahmen, Wolfgang; Micchelli, Charles A. 27 1984 Spectral fractorization of Laurent polynomials. Zbl 0886.65013Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 25 1997 The fundamental theorem of algebra for monosplines satisfying boundary conditions. Zbl 0294.41016Karlin, Samuel; Micchelli, Charles 25 1972 Mathematical aspects of geometric modeling. Zbl 0864.65008Micchelli, Charles A. 25 1995 Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 25 2002 Almost strictly totally positive matrices. Zbl 0752.15016Gasca, M.; Micchelli, Charles A.; Peña, J. M. 23 1992 On refinement equations determined by Pólya frequency sequences. Zbl 0761.42015Goodman, T. N. T.; Micchelli, Charles A. 23 1992 Best \(L^1\) approximation by weak Chebyshev systems and the uniqueness of interpolating perfect splines. Zbl 0339.41022Micchelli, Charles A. 23 1977 Turan formulae and highest precision quadrature rules for Chebyshev coefficients. Zbl 0288.65013Micchelli, C. A.; Rivlin, T. J. 22 1972 Multivariate splines: a probabilistic perspective. Zbl 0623.41014Karlin, S.; Micchelli, C. A.; Rinott, Y. 22 1986 A formula for Kergin interpolation in \(R^ k\). Zbl 0454.41002Micchelli, Charles A.; Milman, Pierre 22 1980 On the approximation order from certain multivariate spline spaces. Zbl 0558.41013Dahmen, Wolfgang; Micchelli, Charles A. 22 1984 Multiscale methods for Fredholm integral equations. Zbl 1332.65188Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 22 2015 Using the refinement equation for the construction of pre-wavelets. V: Extensibility of trigonometric polynomials. Zbl 0765.65023Jia, R.-Q.; Micchelli, C. A. 20 1992 Multiquadratic interpolation improved. Zbl 0764.41001Buhmann, Martin D.; Micchelli, Charles A. 20 1992 On the linear independence of multivariate B-splines. I. Triangulations of simploids. Zbl 0498.41004Dahmen, Wolfgang A.; Micchelli, Charles A. 20 1982 Total positivity and its applications. Meeting, Zaragoza in Jaca, Spain, September 26–30, 1994. Zbl 0884.00045 20 1996 Nonlinear stationary subdivision. Zbl 0902.41001Floater, Michael S.; Micchelli, Charles A. 20 1998 Optimal sequential and non-sequential procedures for evaluating a functional. Zbl 0445.65010Gal, Shmuel; Micchelli, Charles A. 18 1980 A function representation for learning in Banach spaces. Zbl 1078.68129Micchelli, Charles A.; Pontil, Massimiliano 18 2004 On functions which preserve the class of Stieltjes matrices. Zbl 0405.15011Micchelli, Charles A.; Willoughby, R. A. 18 1979 On a numerically efficient method for computing multivariate B-splines. Zbl 0422.41008Micchelli, Charles A. 18 1979 Studies in spline functions and approximation theory. Zbl 0323.00007Karlin, Samuel; Micchelli, Charles A.; Pinkus, Allan; Schoenberg, I. J. 18 1976 A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 18 2012 On spectral learning. Zbl 1242.68201Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 17 2010 Spline spaces are optimal for \(L^2\) n-width. Zbl 0384.41005Melkman, Avraham A.; Micchelli, Charles A. 17 1978 Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces. Zbl 0784.15005Dahmen, Wolfgang; Micchelli, Charles A. 16 1993 Quadrature formulae and Hermite-Birkhoff interpolation. Zbl 0259.41016Micchelli, C. A.; Rivlin, T. J. 16 1973 Weak convergence of the area of nonparametric L//1 surfaces. Zbl 0412.41018Micchelli, Ch. A.; Pinkus, A. 16 1977 On weight functions which admit explicit Gauss-Turán quadrature formulas. Zbl 0853.65027Gori, Laura; Micchelli, Charles A. 15 1996 Using parameters to increase smoothness of curves and surfaces generated by subdivision. Zbl 0711.65007Dyn, Nira; Levin, David; Micchelli, Charles A. 15 1990 Admissible slopes for monotone and convex interpolation. Zbl 0624.41001Edelman, Alan; Micchelli, Charles A. 15 1987 Corner cutting algorithms for the Bézier representation of free form curves. Zbl 0652.41003Goodman, T. N. T.; Micchelli, Charles A. 15 1988 When is there a representer theorem? Vector versus matrix regularizers. Zbl 1235.68128Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 15 2009 Using the refinement equation for the construction of pre-wavelets. III: Elliptic splines. Zbl 0765.65024Micchelli, Charles A.; Rabut, Christophe; Utreras, Florencio I. 14 1991 Chebyshev subspaces and convergence of positive linear operators. Zbl 0268.41008Micchelli, C. A. 14 1973 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012Mhaskar, H. N.; Micchelli, C. A. 14 1994 Continuous refinement equations and subdivision. Zbl 0824.65144Dahmen, Wolfgang; Micchelli, Charles A. 14 1993 Numerical integration rules near Gaussian quadrature. Zbl 0287.65014Micchelli, C. A.; Rivlin, T. J. 13 1974 Convergence of positive linear operators on C(X). Zbl 0294.41032Micchelli, C. A. 13 1975 Statistical encounters with B-splines. Zbl 0615.62021Dahmen, Wolfgang; Micchelli, Charles A. 13 1986 Uncertainty principles in Hilbert spaces. Zbl 1027.47028Goh, Say Song; Micchelli, Charles A. 13 2002 Approximation by radial bases and neural networks. Zbl 0976.65014Li, Xin; Micchelli, Charles A. 13 2000 Some remarks on ridge functions. Zbl 0645.41004Dahmen, Wolfgang; Micchelli, Charles A. 12 1987 Multivariate interpolation and the Radon transform. Zbl 0425.46054Cavaretta, Alfred S. jun.; Micchelli, Charles A.; Sharma, Ambikeshwar 12 1980 Error bounds for learning the kernel. Zbl 1392.68357Micchelli, Charles A.; Pontil, Massimiliano; Wu, Qiang; Zhou, Ding-Xuan 12 2016 Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 12 2009 Functions that preserve families of positive semidefinite matrices. Zbl 0852.43004FitzGerald, Carl H.; Micchelli, Charles A.; Pinkus, Allan 12 1995 Fixed-point proximity algorithm for minimal norm interpolation. Zbl 1440.15015Li, Zheng; Micchelli, Charles A.; Xu, Yuesheng 1 2020 Approximation by translates of a single function of functions in space induced by the convolution with a given function. Zbl 1428.41040Dũng, Dinh; Micchelli, Charles A.; Huy, Vu Nhat 1 2019 Error bounds for learning the kernel. Zbl 1392.68357Micchelli, Charles A.; Pontil, Massimiliano; Wu, Qiang; Zhou, Ding-Xuan 12 2016 Corrigendum to “Multivariate approximation by translates of the Korobov function on Smolyak grids”. Zbl 1382.42005Dũng, Dinh; Micchelli, Charles A. 1 2016 Multiscale methods for Fredholm integral equations. Zbl 1332.65188Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 22 2015 A study on multivariate interpolation by increasingly flat kernel functions. Zbl 1331.41003Lee, Yeon Ju; Micchelli, Charles A.; Yoon, Jungho 4 2015 On convergence of flat multivariate interpolation by translation kernels with finite smoothness. Zbl 1308.41001Lee, Yeon Ju; Micchelli, Charles A.; Yoon, Jungho 8 2014 Proximity algorithms for the L1/TV image denoising model. Zbl 1275.65014Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng; Zeng, Xueying 28 2013 Regularizers for structured sparsity. Zbl 1297.62153Micchelli, Charles A.; Morales, Jean M.; Pontil, Massimiliano 8 2013 Multivariate approximation by translates of the Korobov function on Smolyak grids. Zbl 1305.42006Dũng, Dinh; Micchelli, Charles A. 4 2013 Finite rank kernels for multi-task learning. Zbl 1267.41003Liu, Jianqiang; Micchelli, Charles A.; Wang, Rui; Xu, Yuesheng 2 2013 On computing with the Hilbert spline transform. Zbl 1268.41005Micchelli, Charles A.; Xu, Yuesheng; Yu, Bo 2 2013 On collocation matrices for interpolation and approximation. Zbl 1282.41002Lee, Yeon Ju; Micchelli, Charles A. 2 2013 A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models. Zbl 1273.65085Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 18 2012 The Bedrosian identity for functions analytic in a neighborhood of the unit circle. Zbl 1276.42008Chen, Qiuhui; Micchelli, Charles A. 4 2012 Proximity algorithms for image models: denoising. Zbl 1216.94015Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng 79 2011 On spectral learning. Zbl 1242.68201Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 17 2010 Functions with spline spectra and their applications. Zbl 1186.42014Chen, Qiuhui; Micchelli, Charles A.; Wang, Yi 7 2010 When is there a representer theorem? Vector versus matrix regularizers. Zbl 1235.68128Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 15 2009 Optimal learning of bandlimited functions from localized sampling. Zbl 1180.65182Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 12 2009 Universal multi-task kernels. Zbl 1225.68155Caponnetto, Andrea; Micchelli, Charles A.; Pontil, Massimiliano; Ying, Yiming 33 2008 On translation invariant operators which preserve the B-spline recurrence. Zbl 1283.41010Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 1 2008 On the matrix completion problem for multivariate filter bank construction. Zbl 1128.65111Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng 2 2007 Interpolation filters with prescribed zeros and their refinable functions. Zbl 1214.42074Micchelli, C. A.; Sun, Q. 2 2007 Feature space perspectives for learning the kernel. Zbl 1470.68148Micchelli, Charles A.; Pontil, Massimiliano 2 2007 Universal kernels. Zbl 1222.68266Micchelli, Charles A.; Xu, Yuesheng; Zhang, Haizhang 75 2006 Refinable functions from Blaschke products. Zbl 1134.42337Cotronei, Mariantonia; Lo Cascio, Maria Laura; Kim, Hong Oh; Micchelli, Charles A.; Sauer, Tomas 3 2006 Learning the kernel function via regularization. Zbl 1222.68265Micchelli, Charles A.; Pontil, Massimiliano 64 2005 On learning vector-valued functions. Zbl 1092.93045Micchelli, Charles A.; Pontil, Massimiliano 54 2005 Learning multiple tasks with kernel methods. Zbl 1222.68197Evgeniou, Theodoros; Micchelli, Charles A.; Pontil, Massimiliano 47 2005 Learning convex combinations of continuously parameterized basic kernels. Zbl 1137.68517Argyriou, Andreas; Micchelli, Charles A.; Pontil, Massimiliano 9 2005 Biorthogonal multivariate filter banks from centrally symmetric matrices. Zbl 1079.65141Chen, Qiuhui; Micchelli, Charles A.; Xu, Yuesheng 1 2005 Rao distances. Zbl 1116.62354Micchelli, Charles A.; Noakes, Lyle 1 2005 A function representation for learning in Banach spaces. Zbl 1078.68129Micchelli, Charles A.; Pontil, Massimiliano 18 2004 Multivariate filter banks having matrix factorizations. Zbl 1043.42026Chen, Qiuhui; Micchelli, Charles A.; Peng, Silong; Xu, Yuesheng 6 2003 Refinable functions: positivity and interpolation. Zbl 1071.42025Micchelli, Charles A.; Zhou, Ding-Xuan 1 2003 Continuous refinable functions and self similarity. Zbl 1087.42026Micchelli, Charles A.; Sauer, Thomas 1 2003 Selected papers of Alan J. Hoffman. With commentary. Edited by Charles A. Micchelli. Zbl 1041.01013Hoffman, Alan J. 1 2003 Advances in learning theory. Methods, models and applications. Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, July 8–19, 2002. Zbl 1079.68601Basu, S. 1 2003 Fast collocation methods for second kind integral equations. Zbl 1016.65107Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 52 2002 Discrete wavelet Petrov–Galerkin methods. Zbl 0998.65120Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 25 2002 Uncertainty principles in Hilbert spaces. Zbl 1027.47028Goh, Say Song; Micchelli, Charles A. 13 2002 Refinable functions from their values at integers. Zbl 1035.42036Micchelli, Charles A.; Sun, Qiyu 1 2002 A multilevel method for solving operator equations. Zbl 0990.65059Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 36 2001 Subdivision schemes for iterated function systems. Zbl 0978.54012Micchelli, Charles A.; Sauer, Thomas; Xu, Yuesheng 4 2001 Riesz bases in subspaces of \(L_2 (\mathbb{R}_+)\). Zbl 0997.46024Goodman, T. N. T.; Micchelli, C. A.; Shen, Zuowei 3 2001 Binomial matrices. Zbl 0996.15005Boyd, Geoff; Micchelli, Charles A.; Strang, Gilbert; Zhou, Ding-Xuan 1 2001 Approximation by radial bases and neural networks. Zbl 0976.65014Li, Xin; Micchelli, Charles A. 13 2000 On the Cholesky factorization of the Gram matrix of multivariate functions. Zbl 0977.65024Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 8 2000 Building refinable functions from their values at integers. Zbl 0971.65123de Villiers, Johan M.; Micchelli, Charles A.; Sauer, Thomas 4 2000 Bézout identities with inequality constraints. Zbl 0971.65124Lawton, Wayne M.; Micchelli, Charles A. 2 2000 Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic data. Zbl 0962.65008Micchelli, Charles A.; Olsen, Peder 2 2000 A construction of interpolating wavelets on invariant sets. Zbl 1051.65009Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 33 1999 On vector subdivision. Zbl 0930.65007Micchelli, Charles A.; Sauer, Thomas 35 1998 Nonlinear stationary subdivision. Zbl 0902.41001Floater, Michael S.; Micchelli, Charles A. 20 1998 A construction of refinable sets for interpolating wavelets. Zbl 0921.65097Micchelli, Charles A.; Sauer, Thomas; Xu, Yuesheng 8 1998 On the spectral radius of a bi-infinite periodic and slanted matrix. Zbl 0920.15002Goodman, Tim N. T.; Jia, Rong-Qing; Micchelli, Charles A. 7 1998 On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions. Zbl 0909.65006Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 4 1998 Biorthogonal wavelet expansions. Zbl 0882.65148Dahmen, W.; Micchelli, C. A. 50 1997 The Petrov-Galerkin method for second kind integral equations. II: Multiwavelet schemes. Zbl 0915.65134Chen, Zhongying; Micchelli, Charles A.; Xu, Yuesheng 43 1997 Reconstruction and decomposition algorithms for biorthogonal multiwavelets. Zbl 0872.42010Micchelli, Charles A.; Xu, Yuesheng 38 1997 Regularity of multiwavelets. Zbl 0902.65095Micchelli, C. A.; Sauer, Thomas 37 1997 Wavelet Galerkin methods for second-kind integral equations. Zbl 0913.65129Micchelli, Charles A.; Xu, Yuesheng; Zhao, Yunhe 36 1997 Spectral fractorization of Laurent polynomials. Zbl 0886.65013Goodman, Tim N. T.; Micchelli, Charles A.; Rodriguez, Giuseppe; Seatzu, Sebastiano 25 1997 Sobolev norm convergence of stationary subdivision schemes. Zbl 0937.65148Micchelli, Charles A.; Sauer, Thomas 5 1997 Construction of conjugate quadrature filters with specified zeros. Zbl 0902.65008Lawton, Wayne; Micchelli, Charles A. 4 1997 On a family of filters arising in wavelet construction. Zbl 0866.42026Micchelli, Charles A. 4 1997 On a measure of dissimilarity for normal probability densities. Zbl 1090.62541Micchelli, Charles A. 1 1997 Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos 1 1997 Interpolatory subdivision schemes and wavelets. Zbl 0883.42024Micchelli, Charles A. 32 1996 Total positivity and its applications. Meeting, Zaragoza in Jaca, Spain, September 26–30, 1994. Zbl 0884.00045 20 1996 On weight functions which admit explicit Gauss-Turán quadrature formulas. Zbl 0853.65027Gori, Laura; Micchelli, Charles A. 15 1996 On multivariate splines, matroids, and the ext-functor. Zbl 0908.41004Dahmen, Wolfgang; Dress, Andreas; Micchelli, Charles A. 3 1996 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012Mhaskar, H. N.; Micchelli, Charles A. 49 1995 Mathematical aspects of geometric modeling. Zbl 0864.65008Micchelli, Charles A. 25 1995 Functions that preserve families of positive semidefinite matrices. Zbl 0852.43004FitzGerald, Carl H.; Micchelli, Charles A.; Pinkus, Allan 12 1995 On the Cholesky factorization of the Gram matrix of locally supported functions. Zbl 0833.15010Goodman, T. N. T.; Micchelli, C. A.; Rodriguez, G.; Seatzu, S. 6 1995 Spectral radius formulas for the dilation-convolution integral operator. Zbl 0843.42014Goodman, T. N. T.; Micchelli, Charles; Ward, J. D. 3 1995 Weakly singular Fredholm integral equations. I: Singularity preserving wavelet-Galerkin methods. Zbl 0928.65165Micchelli, Charles A.; Xu, Yuesheng 2 1995 Using the matrix refinement equation for the construction of wavelets on invariant sets. Zbl 0815.42019Micchelli, Charles A.; Xu, Yuesheng 51 1994 Spectral radius formulas for subdivision operators. Zbl 0840.42020Goodman, T. N. T.; Micchelli, Charles A.; Ward, J. D. 46 1994 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012Mhaskar, H. N.; Micchelli, C. A. 14 1994 Using two-slanted matrices for subdivision. Zbl 0802.65003Buhmann, Martin D.; Micchelli, Charles A. 8 1994 Orthonormal cardinal functions. Zbl 0857.42021Goodman, T. N. T.; Micchelli, Charles A. 6 1994 Variational problems arising from balancing several error criteria. Zbl 0809.49021Micchelli, C. A.; Pinkus, A. 4 1994 Banded matrices with banded inverses. III: p-slanted matrices. Zbl 0817.65032Gasca, M.; Micchelli, C. A.; Peña, J. M. 3 1994 Norm estimates for the \(l^ 2\)-inverses of multivariate Toeplitz matrices. Zbl 0790.15024Baxter, 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 0888.42021Micchelli, Charles A.; Xu, Yuesheng 1 1994 Using the refinement equation for evaluating integrals of wavelets. Zbl 0773.65006Dahmen, Wolfgang; Micchelli, Charles A. 58 1993 On linear independence for integer translates of a finite number of functions. Zbl 0790.41016Jia, Rong-Qing; Micchelli, Charles A. 49 1993 Banded matrices with banded inverses. II: Locally finite decomposition of spline spaces. Zbl 0784.15005Dahmen, Wolfgang; Micchelli, Charles A. 16 1993 Continuous refinement equations and subdivision. Zbl 0824.65144Dahmen, Wolfgang; Micchelli, Charles A. 14 1993 Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices. Zbl 0824.65005Barry, Phillip J.; Goldman, Ronald N.; Micchelli, Charles A. 6 1993 Optimal estimation of linear operators from inaccurate data: A second look. Zbl 0794.65052Micchelli, Charles A. 4 1993 Using the refinement equation for the construction of pre-wavelets. IV: Cube splines and elliptic splines united. Zbl 0784.65012Micchelli, Charles A. 1 1993 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015Mhaskar, H. N.; Micchelli, Charles A. 74 1992 Blossoming begets \(B\)-spline bases built better by \(B\)-patches. Zbl 0757.41014Dahmen, Wolfgang; Micchelli, Charles A.; Seidel, Hans-Peter 28 1992 Almost strictly totally positive matrices. Zbl 0752.15016Gasca, M.; Micchelli, Charles A.; Peña, J. M. 23 1992 On refinement equations determined by Pólya frequency sequences. Zbl 0761.42015Goodman, T. N. T.; Micchelli, Charles A. 23 1992 Using the refinement equation for the construction of pre-wavelets. V: Extensibility of trigonometric polynomials. Zbl 0765.65023Jia, R.-Q.; Micchelli, C. A. 20 1992 ...and 141 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,222 Authors 92 Micchelli, Charles A. 53 Xu, Yuesheng 41 Jia, Rong-Qing 37 Dahmen, Wolfgang A. 36 Dyn, Nira 32 Goodman, Timothy N. T. 30 Sauer, Tomas 29 Chui, Charles Kam-tai 29 Conti, Costanza 27 Peña, Juan Manuel 26 Ron, Amos 23 Sun, Qiyu 23 Yoon, Jungho 22 Amat, Sergio P. 22 Pinkus, Allan M. 22 Shen, Lixin 20 Osipenko, Konstantin Yur’evich 20 Romani, Lucia 20 Zhou, Dingxuan 19 Shen, Zuowei 18 Li, Song 17 Chen, Zhongying 17 Ward, Joseph Dinneen 16 Charina, Maria 16 Zhang, Haizhang 15 Buhmann, Martin Dietrich 15 Cao, Feilong 15 Carnicer, Jésus Miguel 15 de Boor, Carl 15 Mazure, Marie-Laurence 15 Protasov, Vladimir Yu. 14 Chen, Dirong 14 Han, Bin 14 Mhaskar, Hrushikesh N. 14 Power, Henry 14 Spalević, Miodrag M. 13 DeVore, Ronald A. 13 Kansa, Edward J. 12 Boyanov, Borislav Dechev 12 Floater, Michael S. 12 Haq, Sirajul 12 Long, Guangqing 12 Manni, Carla 12 Prautzsch, Hartmut 12 Sharma, Ambikeshwar 12 Sheng, Baohuai 12 Wu, Zongmin 12 Zhou, Xinlong 11 Cohen, Albert 11 Goh, Say Song 11 Hon, Yiu-Chung 11 Jetter, Kurt 11 Jiang, Qingtang 11 Lee, Yeon Ju 11 Lu, Jian 11 Milovanović, Gradimir V. 11 Nelakanti, Gnaneshwar 11 Vergne, Michèle 11 Wasilkowski, Grzegorz W. 10 Cotronei, Mariantonia 10 De Villiers, Johan Marthinus 10 Goldman, Ronald N. 10 Liandrat, Jacques 10 San Antolín, Angel 10 Trillo, Juan Carlos 9 Barrera, Domingo 9 Costarelli, Danilo 9 Dahlke, Stephan 9 Daubechies, Ingrid Chantal 9 Gori, Laura 9 Jiang, Ying 9 Li, Xin 9 Lyche, Tom 9 Merrien, Jean-Louis 9 Pereverzev, Sergei V. 9 Plaskota, Leszek 9 Plonka, Gerlind 9 Schaback, Robert 9 Wang, Renhong 9 Woźniakowski, Henryk 9 Yang, Hongqi 8 Barton, Michael H. 8 Beccari, Carolina Vittoria 8 Casciola, Giulio 8 Chen, Jian 8 Chen, Qiuhui 8 Fornberg, Bengt 8 Guillot, Dominique 8 Khare, Apoorva 8 Lai, Mingjun 8 Magaril-Il’yaev, Gregoriĭ Geogrievich 8 Maleknejad, Khosrow 8 Mathé, Peter 8 Menegatto, Valdir Antonio 8 Novak, Erich 8 Oswald, Peter 8 Parfënov, O. G. 8 Pitolli, Francesca 8 Rivlin, Theodore Joseph 8 Sablonnière, Paul ...and 3,122 more Authors all top 5 Cited in 394 Serials 269 Journal of Approximation Theory 164 Journal of Computational and Applied Mathematics 118 Advances in Computational Mathematics 101 Computer Aided Geometric Design 97 Applied and Computational Harmonic Analysis 87 Applied Mathematics and Computation 82 Computers & Mathematics with Applications 78 Constructive Approximation 77 Linear Algebra and its Applications 70 Journal of Mathematical Analysis and Applications 69 Journal of Complexity 60 Engineering Analysis with Boundary Elements 59 Mathematics of Computation 55 Numerical Algorithms 40 Applied Numerical Mathematics 37 Numerische Mathematik 37 Proceedings of the American Mathematical Society 33 Transactions of the American Mathematical Society 32 Computer Methods in Applied Mechanics and Engineering 30 Mathematical Notes 30 Numerical Functional Analysis and Optimization 29 BIT 28 Machine Learning 27 Journal of Computational Physics 27 Journal of Scientific Computing 27 The Journal of Fourier Analysis and Applications 27 International Journal of Wavelets, Multiresolution and Information Processing 25 International Journal of Computer Mathematics 25 Acta Mathematica Sinica. 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