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Soft computing (Berlin, Germany), ISSN 1433-7479, 05/2015, Volume 20, Issue 8, pp. 3283 - 3302

.... In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability...

Engineering | Computational Intelligence | Gramâ€“Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel Hilbert space method | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Strongly generalized differentiability | Fuzzy differential equations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology | Methods | Differential equations | Resveratrol

Engineering | Computational Intelligence | Gramâ€“Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel Hilbert space method | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Strongly generalized differentiability | Fuzzy differential equations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology | Methods | Differential equations | Resveratrol

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2010, Volume 38, Issue 6, pp. 3412 - 3444

.... By developing a tool on simultaneous diagonalization of two positive definite kernels, we obtain shaper results on the minimax rates of convergence and show that smoothness regularized estimators...

Covariance | Sample size | Linear regression | Eigenvalues | Eigenfunctions | Hilbert spaces | Polynomials | Sobolev spaces | Estimators | Estimation methods | Minimax | Reproducing kernel Hilbert space | Functional linear regression | Sobolev space | Eigenfunction | Sacks-Ylvisaker conditions | Slope function | Eigenvalue | Optimal convergence rate | Simultaneous diagonalization | Principal component analysis | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Regularization methods | Hilbert space | Regression analysis | Convergence | Sacksâ€“Ylvisaker conditions | 62J05 | eigenfunction | optimal convergence rate | functional linear regression | slope function | 62G20 | reproducing kernel Hilbert space | eigenvalue | minimax | principal component analysis | simultaneous diagonalization

Covariance | Sample size | Linear regression | Eigenvalues | Eigenfunctions | Hilbert spaces | Polynomials | Sobolev spaces | Estimators | Estimation methods | Minimax | Reproducing kernel Hilbert space | Functional linear regression | Sobolev space | Eigenfunction | Sacks-Ylvisaker conditions | Slope function | Eigenvalue | Optimal convergence rate | Simultaneous diagonalization | Principal component analysis | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Regularization methods | Hilbert space | Regression analysis | Convergence | Sacksâ€“Ylvisaker conditions | 62J05 | eigenfunction | optimal convergence rate | functional linear regression | slope function | 62G20 | reproducing kernel Hilbert space | eigenvalue | minimax | principal component analysis | simultaneous diagonalization

Journal Article

Artificial Intelligence Review, ISSN 0269-2821, 10/2019, Volume 52, Issue 3, pp. 2039 - 2059

Modeling policies in reproducing kernel Hilbert space (RKHS) offers a very flexible and powerful new family of policy gradient algorithms called RKHS policy gradient algorithms...

Reproducing kernel Hilbert space | Policy gradient | Non-parametric | Artificial Intelligence | Computer Science | Reinforcement learning | Computer Science, general | Policy search | Importance sampling | Computer Science, Artificial Intelligence | Technology | Science & Technology | Computer science | Algorithms | Artificial intelligence | Analysis | Kernels | Domains | Policies | Hilbert space | Modelling | Regularization | Sampling techniques

Reproducing kernel Hilbert space | Policy gradient | Non-parametric | Artificial Intelligence | Computer Science | Reinforcement learning | Computer Science, general | Policy search | Importance sampling | Computer Science, Artificial Intelligence | Technology | Science & Technology | Computer science | Algorithms | Artificial intelligence | Analysis | Kernels | Domains | Policies | Hilbert space | Modelling | Regularization | Sampling techniques

Journal Article

Advances in computational mathematics, ISSN 1572-9044, 10/2018, Volume 45, Issue 2, pp. 869 - 896

.... The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS...

Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Mathematics | Reproducing kernel Hilbert spaces | Mathematical Modeling and Industrial Mathematics | Adaptive estimation | Computational Science and Engineering | Distributed parameter systems | Physical Sciences | Mathematics, Applied | Science & Technology | Hilbert space | Research | Kernel functions | Differential equations, Nonlinear | Mathematical research | Economic models | Adaptive systems | Parameter estimation | Nonlinear equations | Nonlinear differential equations | Exponential functions | Estimates | Multiresolution analysis | Convergence | Kernels | Multiscale analysis | Ordinary differential equations | Dimensional stability | Nonlinear systems

Visualization | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Mathematics | Reproducing kernel Hilbert spaces | Mathematical Modeling and Industrial Mathematics | Adaptive estimation | Computational Science and Engineering | Distributed parameter systems | Physical Sciences | Mathematics, Applied | Science & Technology | Hilbert space | Research | Kernel functions | Differential equations, Nonlinear | Mathematical research | Economic models | Adaptive systems | Parameter estimation | Nonlinear equations | Nonlinear differential equations | Exponential functions | Estimates | Multiresolution analysis | Convergence | Kernels | Multiscale analysis | Ordinary differential equations | Dimensional stability | Nonlinear systems

Journal Article

Neural computing & applications, ISSN 1433-3058, 12/2015, Volume 28, Issue 7, pp. 1591 - 1610

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm...

Data Mining and Knowledge Discovery | Reproducing kernel Hilbert space method | 47B32 | Fuzzy integrodifferential equations | Computational Science and Engineering | Strongly generalized differentiability | Computational Biology/Bioinformatics | Gramâ€“Schmidt process | Computer Science | Image Processing and Computer Vision | 34K28 | Artificial Intelligence (incl. Robotics) | 46S40 | Probability and Statistics in Computer Science | Computer Science, Artificial Intelligence | Technology | Science & Technology | Annealing | Algorithms | Scheduling | Hilbert space | Kernel functions | Computer simulation | Simulated annealing | Adaptation

Data Mining and Knowledge Discovery | Reproducing kernel Hilbert space method | 47B32 | Fuzzy integrodifferential equations | Computational Science and Engineering | Strongly generalized differentiability | Computational Biology/Bioinformatics | Gramâ€“Schmidt process | Computer Science | Image Processing and Computer Vision | 34K28 | Artificial Intelligence (incl. Robotics) | 46S40 | Probability and Statistics in Computer Science | Computer Science, Artificial Intelligence | Technology | Science & Technology | Annealing | Algorithms | Scheduling | Hilbert space | Kernel functions | Computer simulation | Simulated annealing | Adaptation

Journal Article

The Annals of statistics, ISSN 0090-5364, 12/2010, Volume 38, Issue 6, pp. 3660 - 3695

.... The complexity penalty is determined jointly by the empirical Lâ‚‚ norms and the reproducing kernel Hilbert space (RKHS...

Minimax | Machine learning | Eigenvalues | Mathematical constants | Hilbert spaces | Mathematical vectors | Mathematical functions | Sobolev spaces | Estimators | Oracles | Multiple kernel learning | Restricted isometry | High dimensionality | Reproducing kernel Hilbert spaces | Oracle inequality | Sparsity | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Regularization methods | Hilbert space | multiple kernel learning | 62G08 | restricted isometry | 62J07 | oracle inequality | sparsity | 62F12 | reproducing kernel Hilbert spaces

Minimax | Machine learning | Eigenvalues | Mathematical constants | Hilbert spaces | Mathematical vectors | Mathematical functions | Sobolev spaces | Estimators | Oracles | Multiple kernel learning | Restricted isometry | High dimensionality | Reproducing kernel Hilbert spaces | Oracle inequality | Sparsity | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Regularization methods | Hilbert space | multiple kernel learning | 62G08 | restricted isometry | 62J07 | oracle inequality | sparsity | 62F12 | reproducing kernel Hilbert spaces

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 2180-4206, 10/2014, Volume 38, Issue 1, pp. 271 - 287

In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order...

Reproducing kernel method | 34B15 | Bratuâ€™s problem | 46E22 | 47B32 | Mathematics, general | Mathematics | Applications of Mathematics | Series solutions | Reproducing kernel space | 74S30 | 30E25 | Physical Sciences | Science & Technology | Boundary value problems | Hilbert space | Decomposition | Shooting | Differential equations

Reproducing kernel method | 34B15 | Bratuâ€™s problem | 46E22 | 47B32 | Mathematics, general | Mathematics | Applications of Mathematics | Series solutions | Reproducing kernel space | 74S30 | 30E25 | Physical Sciences | Science & Technology | Boundary value problems | Hilbert space | Decomposition | Shooting | Differential equations

Journal Article

The Annals of statistics, ISSN 0090-5364, 06/2008, Volume 36, Issue 3, pp. 1171 - 1220

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS...

Approximation | Machine learning | Dot product of vectors | Hilbert spaces | Principal components analysis | Mathematical vectors | Mathematical functions | Mathematics | Learning theory | Modeling | Support vector machines | Graphical models | Reproducing kernels | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Algorithms | Linear programming | Nonlinear programming | Estimating techniques | Artificial intelligence | support vector machines | 68T05 | reproducing kernels | graphical models | 30C40

Approximation | Machine learning | Dot product of vectors | Hilbert spaces | Principal components analysis | Mathematical vectors | Mathematical functions | Mathematics | Learning theory | Modeling | Support vector machines | Graphical models | Reproducing kernels | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Algorithms | Linear programming | Nonlinear programming | Estimating techniques | Artificial intelligence | support vector machines | 68T05 | reproducing kernels | graphical models | 30C40

Journal Article

Complex analysis and operator theory, ISSN 1661-8254, 2/2019, Volume 13, Issue 1, pp. 193 - 221

...) space, which turns out also a reproducing kernel Hilbert space.

Operator Theory | 46E22 | Analysis | Mathematics, general | Hilbert spaces | Mathematics | Reproducing kernels | Isoperimetric inequality | Brunâ€“Minkowski inequality | Physical Sciences | Mathematics, Applied | Science & Technology | Kernels | Hilbert space | Quantum theory

Operator Theory | 46E22 | Analysis | Mathematics, general | Hilbert spaces | Mathematics | Reproducing kernels | Isoperimetric inequality | Brunâ€“Minkowski inequality | Physical Sciences | Mathematics, Applied | Science & Technology | Kernels | Hilbert space | Quantum theory

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2012, Volume 40, Issue 5, pp. 2483 - 2510

..., such as a reproducing kernel Hubert space of smooth functions. This model includes time and frequency sampling as special cases...

Minimax | Eigenvalues | Linear transformations | Principal components analysis | Hilbert spaces | Eigenfunctions | Mathematical vectors | Modeling | Estimators | Truncation | Time sampling | Linear sampling operator | Reproducing kernel Hilbert space | Fourier truncation | Functional principal component analysis | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical functions | Sampling | Estimates | linear sampling operator | 62G05 | 41A35 | 41A25 | reproducing kernel Hilbert space | 62H12 | time sampling | 62H25

Minimax | Eigenvalues | Linear transformations | Principal components analysis | Hilbert spaces | Eigenfunctions | Mathematical vectors | Modeling | Estimators | Truncation | Time sampling | Linear sampling operator | Reproducing kernel Hilbert space | Fourier truncation | Functional principal component analysis | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical functions | Sampling | Estimates | linear sampling operator | 62G05 | 41A35 | 41A25 | reproducing kernel Hilbert space | 62H12 | time sampling | 62H25

Journal Article

Foundations and trends in signal processing, ISSN 1932-8346, 2014, Volume 8, Issue 1-2, pp. 1 - 126

Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces...

Kernels | Foundations | Euclidean geometry | Effectiveness | Linear algebra | Signal processing | Hilbert space | Trends

Kernels | Foundations | Euclidean geometry | Effectiveness | Linear algebra | Signal processing | Hilbert space | Trends

Journal Article

1982, ISBN 9780879334345, Volume 25., xiii, 654

Book

Applied mathematics and computation, ISSN 0096-3003, 05/2013, Volume 219, Issue 17, pp. 8938 - 8948

In this study, the numerical solution of Fredholm integroâ€“differential equation is discussed in a reproducing kernel Hilbert space...

Reproducing kernel Hilbert space | Fredholm integroâ€“differential equation | Exact solution | Fredholm integro-differential equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Methods | Differential equations

Reproducing kernel Hilbert space | Fredholm integroâ€“differential equation | Exact solution | Fredholm integro-differential equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Methods | Differential equations

Journal Article

Neural computing & applications, ISSN 0941-0643, 7/2019, Volume 31, Issue 7, pp. 2233 - 2241

.... The method is based on reproducing kernel Hilbert spaces in the framework of the standard pseudospectral method...

Computational Biology/Bioinformatics | Reproducing kernel Hilbert space | Pseudospectral method | Capillary formation | Artificial Intelligence | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Computational Science and Engineering | Tumor angiogenic factor | Probability and Statistics in Computer Science | Computer Science, Artificial Intelligence | Technology | Science & Technology | Models | Analysis | Methods | Investigations | Tumors | Kernels | Angiogenesis | Mathematical analysis | Two dimensional models | Boundary conditions | Mathematical models | Hilbert space | Matrix methods | Spectral methods

Computational Biology/Bioinformatics | Reproducing kernel Hilbert space | Pseudospectral method | Capillary formation | Artificial Intelligence | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Computational Science and Engineering | Tumor angiogenic factor | Probability and Statistics in Computer Science | Computer Science, Artificial Intelligence | Technology | Science & Technology | Models | Analysis | Methods | Investigations | Tumors | Kernels | Angiogenesis | Mathematical analysis | Two dimensional models | Boundary conditions | Mathematical models | Hilbert space | Matrix methods | Spectral methods

Journal Article

Complex analysis and operator theory, ISSN 1661-8254, 4/2019, Volume 13, Issue 3, pp. 879 - 892

.... We show that a composition operator is bounded on the Hardy space
$$H^2(\mathbb {D}^2)$$
H
2
(
D
2
)
if some associated function is a positive kernel...

Reproducing kernel | Secondary 47B32 | Operator Theory | Analysis | Composition operator | Mathematics, general | Primary 47B33 | Mathematics | Hardy space | Physical Sciences

Reproducing kernel | Secondary 47B32 | Operator Theory | Analysis | Composition operator | Mathematics, general | Primary 47B33 | Mathematics | Hardy space | Physical Sciences