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1. Full Text Sampling methods for the Nyström method
by Kumar, Sanjiv and Mohri, Mehryar and Talwalkar, Ameet
Journal of Machine Learning Research, ISSN 1532-4435, 04/2012, Volume 13, pp. 981 - 1006
The Nystrom method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect... 
Nyström method | Large-scale learning | Ensemble methods | Low-rank approximation | large-scale learning | MATRIX | ensemble methods | nystrom method | ALGORITHMS | low-rank approximation | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
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2. Full Text Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion
by Betz, Wolfgang and Papaioannou, Iason and Straub, Daniel
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2014, Volume 271, pp. 109 - 129
The computational efficiency of random field representations with the Karhunen–Loève (KL) expansion relies on the solution of a Fredholm integral eigenvalue... 
Nyström method | Finite cell method | Galerkin method | Random field discretization | Collocation method | Karhunen–Loève expansion | Karhunen-Loève expansion | Nystrom method | GAUSSIAN TRANSLATION PROCESSES | IMPLEMENTATION | EQUATIONS | SIMULATION | ELEMENTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MATRICES | SOLID MECHANICS | Karhunen-Loeve expansion | Finite element method | Analysis | Methods | Run time (computers) | Mathematical analysis | Eigenvalues | Projection | Mathematical models | Mesh generation | Galerkin methods
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3. Full Text Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods
by Monovasilis, T and Kalogiratou, Z and Simos, T.E
Mediterranean Journal of Mathematics, ISSN 1660-5446, 08/2016, Volume 13, Issue 4, pp. 2271 - 2285
In this work, we give the general framework for constructing trigonometrically fitted symplectic Runge-Kutta-Nystrom (RKN) methods from symplectic... 
65L05 | Runge-Kutta-Nystrom methods | MATHEMATICS | Hamiltonian systems | MATHEMATICS, APPLIED | FREQUENCY EVALUATION | Partitioned Runge-Kutta methods | ODES | NUMERICAL-INTEGRATION | symplectic methods | trigonometrical fitting | OSCILLATING SOLUTIONS | INITIAL-VALUE PROBLEMS | Computer science | International trade | Methods | Resveratrol
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4. Full Text Predictive Nyström method for kernel methods
by Wu, Jiangang and Ding, Lizhong and Liao, Shizhong
Neurocomputing, ISSN 0925-2312, 04/2017, Volume 234, pp. 116 - 125
Nyström method is a widely used matrix approximation method for scaling up kernel methods, and existing sampling strategies for Nyström method are proposed to... 
Nyström method | Matrix approximation | Kernel methods | Predictive sampling strategy | Nystrom method | MONTE-CARLO ALGORITHMS | MATRIX DECOMPOSITIONS | SVD | APPROXIMATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Computer science | Methods
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5. Full Text Spectral grouping using the Nystrom method
by Fowlkes, C and Belongie, S and Chung, F and Malik, J
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 02/2004, Volume 26, Issue 2, pp. 214 - 225
Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation. However, due to the computational demands of these... 
Image segmentation | Histograms | Image resolution | Layout | Prototypes | Eigenvalues and eigenfunctions | Graph theory | Spatiotemporal phenomena | Partitioning algorithms | Pixel | Image and video segmentation | Normalized cuts | Clustering | Nyström approximation | Spectral graph theory | MACHINES | MOTION | normalized cuts | Nystrom approximation | image and video segmentation | SEGMENTATION | clustering | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | spectral graph theory | ENGINEERING, ELECTRICAL & ELECTRONIC | User-Computer Interface | Reproducibility of Results | Information Storage and Retrieval - methods | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Subtraction Technique | Computer Graphics | Algorithms | Numerical Analysis, Computer-Assisted | Sensitivity and Specificity | Video Recording - methods | Signal Processing, Computer-Assisted | Image Enhancement - methods | Pattern Recognition, Automated | Cluster Analysis | Object recognition (Computers) | Research | Pattern recognition
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6. Full Text Construction of an optimized explicit Runge–Kutta–Nyström method for the numerical solution of oscillatory initial value problems
by Kosti, A.A and Anastassi, Z.A and Simos, T.E
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 11, pp. 3381 - 3390
An explicit optimized Runge–Kutta–Nyström method with four stages and fifth algebraic order is developed. The produced method has variable coefficients with... 
Runge–Kutta–Nyström methods | Initial value problems | Phase-lag | Numerical solution | Explicit methods | Amplification factor | RungeKuttaNystrm methods | Runge-Kutta-Nystrom methods | MATHEMATICS, APPLIED
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7. Full Text A fourth order modified trigonometrically fitted symplectic Runge–Kutta–Nyström method
by Kalogiratou, Z and Monovasilis, Th and Simos, T.E
Computer Physics Communications, ISSN 0010-4655, 12/2014, Volume 185, Issue 12, pp. 3151 - 3155
In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the fourth order five stages method of Calvo and... 
Symplectic methods | Hamiltonian systems | Runge Kutta Nyström methods | Exponential fitting | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Runge Kutta Nystrom methods | Computer science | International trade | Methods | Construction | Numerical integration | Computer simulation | Nonlinearity | Mathematical models | Runge-Kutta method | Two dimensional | Harmonic oscillators
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8. A modified runge-kutta-nyström method by using phase lag properties for the numerical solution of orbital problems
by Papadopoulos, Dimitris F and Simos, T.E
Applied Mathematics and Information Sciences, ISSN 1935-0090, 2013, Volume 7, Issue 2, pp. 433 - 437
In this paper, a new modified Runge-Kutta-Nystrom method of third algebraic order is developed. The new modified RKN method has phase-lag and amplification... 
Oscillating solution | Initial value problems | Derivatives | Phase-fitted'8Amplification-fitted | Orbital problems | Runge-kutta-nyström methods | 2ND-ORDER IVPS | MATHEMATICS, APPLIED | initial value problems | oscillating solution | PHYSICS, MATHEMATICAL | Phase-fitted | RADIAL SCHRODINGER-EQUATION | Runge-Kutta-Nystrom methods | derivatives | TRIGONOMETRICALLY-FITTED METHODS | ORDER | Amplification-fitted | OSCILLATING SOLUTIONS
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9. Full Text Constrained Locally Corrected Nyström Method
by Hendijani, Nastaran and Jin Cheng and Adams, Robert J and Young, John C
IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 07/2015, Volume 63, Issue 7, pp. 3111 - 3121
A generalization of the locally corrected Nyström (LCN) discretization method is outlined wherein sparse transformations of the LCN system matrix are obtained... 
Geometry | numerical methods | Integral equations | Null space | moment method | Polynomials | locally corrected Nyström method | Sparse matrices | Impedance | Method of moments | DISCRETIZATION | MODES | FIELD INTEGRAL-EQUATION | TELECOMMUNICATIONS | SCATTERING | Locally corrected Nystrom (LCN) method | ENGINEERING, ELECTRICAL & ELECTRONIC | Transformations (Mathematics) | Numerical analysis | Research | Engineering research | Singular value decomposition
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10. Full Text On the Nyström method for approximating a Gram matrix for improved kernel-based learning
by Drineas, Petros and Mahoney, Michael W
Journal of Machine Learning Research, ISSN 1533-7928, 12/2005, Volume 6, pp. 2153 - 2175
A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n(3)), where n is the number of training... 
Nyström method | Kernel methods | Randomized algorithms | Gram matrix | Nystrom method | DIMENSIONALITY REDUCTION | randomized algorithms | kernel methods | EIGENMAPS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
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11. Full Text A five–stages symmetric method with improved phase properties
by Liu, Chenglian and Simos, T E
Journal of Mathematical Chemistry, ISSN 0259-9791, 4/2018, Volume 56, Issue 4, pp. 1313 - 1338
In this paper, for the first time in the literature, we introduce a new five–stages symmetric two–step method with improved phase and stability properties. The... 
65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | INITIAL-VALUE-PROBLEMS | CHEMISTRY, MULTIDISCIPLINARY | RADIAL SCHRODINGER-EQUATION | TRIGONOMETRICALLY-FITTED FORMULAS | FINITE-DIFFERENCE PAIR | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | KUTTA-NYSTROM METHODS | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | 2-STEP HYBRID METHODS | Numerical analysis | Research | Mathematical research | Differential equations | Symmetry
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12. Full Text A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
by Anastassi, Z.A and Simos, T.E
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2012, Volume 236, Issue 16, pp. 3880 - 3889
In this article, we develop an explicit symmetric linear phase-fitted four-step method with a free coefficient as parameter. The parameter is used for the... 
Symmetric linear multistep methods | Ordinary differential equations | Phase fitting | Numerical solution | Schrödinger equation | Finite difference methods | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | HIGH-ORDER | PHASE-LAG | TRIGONOMETRICALLY-FITTED METHODS | SCHEME | NUMERICAL-SOLUTION | IVPS | Schrodinger equation | MULTISTEP METHODS | 2-STEP | NYSTROM METHOD | Intervals | Computation | Mathematical analysis | Truncation errors | Mathematical models | Schroedinger equation | Coefficients | Optimization
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13. Full Text An eight-step semi-embedded predictor–corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown
by Panopoulos, G.A and Simos, T.E
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2015, Volume 290, pp. 1 - 15
Our new linear symmetric semi-embedded predictor–corrector method (SEPCM) presented here is based on the multistep symmetric method of Quinlan and Tremaine... 
Second-order IVPs | Multistep | Predictor–corrector | Orbital problems | Kepler problem | Semi-embedded | MATHEMATICS, APPLIED | METHOD EPCM | 2ND-ORDER DIFFERENTIAL-EQUATIONS | STABILITY | RADIAL SCHRODINGER-EQUATION | SOLVING PERTURBED OSCILLATORS | INITIAL-VALUE PROBLEMS | NUMERICAL-SOLUTION | MULTISTEP METHODS | CONSTRUCTION | Predictor-corrector | KUTTA-NYSTROM METHODS | Predictor-corrector methods | Construction | Algebra | Computation | Constants | Initial value problems | Mathematical models | Symmetry
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14. Full Text Nystrom subsampling method for coefficient-based regularized regression
by Ma, LD and Shi, L and Wu, ZM
INVERSE PROBLEMS, ISSN 0266-5611, 07/2019, Volume 35, Issue 7, p. 75002
Kernel methods are attractive in data analysis as they can model nonlinear similarities between observations and provide means to rich representations, both of... 
RATES | MATHEMATICS, APPLIED | mini-max optimal rates | Nystrom subsampling method | indefinite kernels | PHYSICS, MATHEMATICAL | coefficient-based regularized regression | KERNELS
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15. Full Text Method of analytical regularization in computational photonics
by Nosich, Alexander I
Radio Science, ISSN 0048-6604, 08/2016, Volume 51, Issue 8, pp. 1421 - 1430
We discuss the advantages of the conversion of electromagnetic field problems to the Fredholm second‐kind integral equations (analytical regularization) and... 
analytical regularization leads to convergent numerical solutions | optical wavelength range requires impedance or dielectric boundary conditions | singular integral equations provide adequate foundation for advanced numerical analysis | INTEGRAL-EQUATION | OBLIQUE-INCIDENCE | GEOCHEMISTRY & GEOPHYSICS | REMOTE SENSING | ASTRONOMY & ASTROPHYSICS | DIFFRACTION | CONVERGING NYSTROM METHODS | TELECOMMUNICATIONS | METEOROLOGY & ATMOSPHERIC SCIENCES | SCATTERING | LINES | LAYERED MEDIA | Magnetic fields | Integral equations | Dielectrics | Wavelengths | Singular integral equations | Mathematical analysis | Electromagnetic fields | Regularization | Conversion
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16. Full Text A high algebraic order predictor–corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems
by Alolyan, Ibraheem and Simos, T E
Journal of Mathematical Chemistry, ISSN 0259-9791, 8/2015, Volume 53, Issue 7, pp. 1495 - 1522
In this paper an eighth algebraic order predictor–corrector explicit four-step method is studied. The main scope of this paper is to study the consequences of... 
65L05 | Explicit methods | Predictor–corrector methods | Phase-fitted | Schrödinger equation | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | Predictor-corrector methods | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | MULTIDERIVATIVE METHODS | 4-STEP METHODS | NYSTROM METHOD | SYMMETRIC MULTISTEP METHODS
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17. Full Text Revisiting the Nyström method for improved large-scale machine learning
by Gittens, Alex and Mahoney, Michael W
Journal of Machine Learning Research, ISSN 1532-4435, 04/2016, Volume 17, pp. 1 - 65
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices... 
Kernel methods | Randomized algorithms | Low-rank approximation | Nyström approximation | Numerical linear algebra | APPROXIMATION | Nystrom approximation | RANDOMIZED HADAMARD-TRANSFORM | ALGORITHMS | low-rank approximation | IDENTIFICATION | SOLVER | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | numerical linear algebra | MATRIX DECOMPOSITIONS | randomized algorithms | kernel methods | AUTOMATION & CONTROL SYSTEMS
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18. Full Text A new family of 7 stages, eighth‐order explicit Numerov‐type methods
by Simos, T.E and Tsitouras, Ch
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7867 - 7878
In this paper, we consider the integration of the special second‐order initial value problem. Hybrid Numerov methods are used, which are constructed in the... 
numerical solution | interval of periodicity | hybrid Numerov methods | constant coefficients | initial value problem | phase‐lag | Interval of periodicity | Hybrid Numerov methods | Phase-lag | Constant coefficients | Numerical solution | Initial value problem | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | INITIAL-VALUE-PROBLEMS | SCHRODINGER-EQUATION | phase-lag | VANISHED PHASE-LAG | KUTTA-NYSTROM METHODS | NUMERICAL-INTEGRATION | P-STABLE METHOD | 2-STEP HYBRID METHODS | NOUMEROV-TYPE METHOD | OSCILLATING SOLUTIONS | Construction standards | Boundary value problems | Runge-Kutta method | Phase lag | Construction methods
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