2017
Reconstruction of normal forms by learning informed observation geometries from data
Yair O, Talmon R, Coifman RR, Kevrekidis IG. Reconstruction of normal forms by learning informed observation geometries from data. Proceedings Of The National Academy Of Sciences Of The United States Of America 2017, 114: e7865-e7874. PMID: 28831006, PMCID: PMC5617245, DOI: 10.1073/pnas.1620045114.Peer-Reviewed Original ResearchNormal formNonlinear differential equationsDynamical systems theoryAppropriate normal formFundamental physical quantitiesDifferential equationsDynamical regimesState variablesPhysical quantitiesPhysical lawsSystems theoryGeometry learningEmpirical observationsObservation geometryHeart of scienceDynamicsPrior knowledgeEquationsRealizationLawParametersGeometryTheoryExplicit referenceForm
2015
Information Integration, Organization, and Numerical Harmonic Analysis
Coifman R, Talmon R, Gavish M, Haddad A. Information Integration, Organization, and Numerical Harmonic Analysis. 2015, 254-271. DOI: 10.1002/9781118853887.ch10.Peer-Reviewed Original ResearchPartial differential equationsHarmonic analysisLocal linear modelsLocal similarity modelNumerical harmonic analysisDifferential equationsMathematical frameworkNewtonian calculusGlobal solutionClassical toolsFunctional regressionLinear modelData matrixUnrelated approachesMathematicsSignal processingNumericsEquationsMachine learningGraphGlobal configurationCalculusData analysisGeometryModel
1998
Multiscale Inversion of Elliptic Operators
Averbuch A, Beylkin G, Coifman R, Israeli M. Multiscale Inversion of Elliptic Operators. Wavelet Analysis And Its Applications 1998, 7: 341-359. DOI: 10.1016/s1874-608x(98)80013-7.Peer-Reviewed Original ResearchLinear systemsCondition numberElliptic partial differential equationsPartial differential equationsLarge condition numberBoundary conditionsConjugate gradient iterationNumber of iterationsFast adaptive algorithmNumber of operationsDifferential equationsWavelet coordinatesSuch equationsMultiscale inversionDifferential operatorsElliptic operatorsDiagonal preconditionerComplicated equationsPeriodic boundary conditionsGradient iterationPoisson equationGradient algorithmConjugate directionsEquationsAdaptive algorithm
1993
The fast multipole method for the wave equation: a pedestrian prescription
Coifman R, Rokhlin V, Wandzura S. The fast multipole method for the wave equation: a pedestrian prescription. IEEE Antennas And Propagation Magazine 1993, 35: 7-12. DOI: 10.1109/74.250128.Peer-Reviewed Original ResearchThe Inverse Spectral Method on the Plane
Coifman R, Fokas A. The Inverse Spectral Method on the Plane. Springer Series In Nonlinear Dynamics 1993, 58-85. DOI: 10.1007/978-3-642-58045-1_5.Peer-Reviewed Original ResearchWavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
Alpert B, Beylkin G, Coifman R, Rokhlin V. Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations. SIAM Journal On Scientific Computing 1993, 14: 159-184. DOI: 10.1137/0914010.Peer-Reviewed Original ResearchIntegral equationsSecond kind integral equationsKind integral equationsWavelet-like basisVector space basisIntegral operatorsNumerical solutionNumber of pointsFinite numberFast solutionSparse matricesNumerical resultsDiscretizationEquationsOperatorsSparse representationSingularitySolutionGeneralizationThe fast multipole method for electromagnetic scattering calculations
Coifman R, Rokhlin V, Wandzura S. The fast multipole method for electromagnetic scattering calculations. 1993, 48-51 vol.1. DOI: 10.1109/aps.1993.385405.Peer-Reviewed Original ResearchFast multipole methodMultipole methodDense impedance matrixThree-dimensional electromagnetic problemsBoundary integral equationsAccurate numerical modelingMethod of momentsIntegral equationsElectromagnetic problemsElectromagnetic scattering calculationsRadiation problemsElementary derivationPhysical interpretationImpedance matrixComputational complexityElectromagnetic scatteringScattering calculationsNumerical modelingSparse decompositionEquationsProblemDerivationMomentModelingCalculations
1990
Wavelets for the Fast Solution of Second-Kind Integral Equations
Alpert B, Beylkin G, Coifman R, Rokhlin V. Wavelets for the Fast Solution of Second-Kind Integral Equations. 1990 DOI: 10.21236/ada233650.Peer-Reviewed Original ResearchIntegral equationsSecond kind integral equationsKind integral equationsNon-oscillatory kernelsVector space basisIntegral operatorsNumerical solutionNumber of pointsFinite numberFast solutionSparse matricesNumerical resultsDiscretizationEquationsOperatorsSparse representationSingularitySolutionGeneralizationKernel
1989
Linear spectral problems, non-linear equations and the δ-method
Beals R, Coifman R. Linear spectral problems, non-linear equations and the δ-method. Inverse Problems 1989, 5: 87. DOI: 10.1088/0266-5611/5/2/002.Peer-Reviewed Original Research
1986
The D-bar approach to inverse scattering and nonlinear evolutions
Beals R, Coifman R. The D-bar approach to inverse scattering and nonlinear evolutions. Physica D Nonlinear Phenomena 1986, 18: 242-249. DOI: 10.1016/0167-2789(86)90184-3.Peer-Reviewed Original ResearchSelf-dual Yang-Mills equationsComplex differential equationsYang-Mills equationsInverse scattering methodDavey–StewartsonDifferential equationsNonlinear equationsSchrödinger equationAssociated hierarchyInverse scatteringNonlinear evolutionEquationsMultidimensional problemsScattering methodInversionProblemR3Scattering