Kernel based quadrature on spheres and other homogeneous spaces
暂无分享,去创建一个
Joseph D. Ward | Grady B. Wright | Francis J. Narcowich | Edward J. Fuselier | Thomas Hangelbroek | G. Wright | J. Ward | E. Fuselier | T. Hangelbroek | F. Narcowich
[1] Simon Hubbert,et al. Radial basis functions for the sphere , 2015 .
[2] Joseph D. Ward,et al. Localized Bases for Kernel Spaces on the Unit Sphere , 2012, SIAM J. Numer. Anal..
[3] Gene H. Golub,et al. Numerical solution of saddle point problems , 2005, Acta Numerica.
[4] F. Giraldo. Lagrange-Galerkin Methods on Spherical Geodesic Grids , 1997 .
[5] Hrushikesh Narhar Mhaskar,et al. L BERNSTEIN ESTIMATES AND APPROXIMATION BY SPHERICAL BASIS FUNCTIONS , 2010 .
[6] Alan Edelman,et al. The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..
[7] N. Vilenkin. Special Functions and the Theory of Group Representations , 1968 .
[8] Joseph D. Ward,et al. Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation , 2010, Foundations of Computational Mathematics.
[9] Emmanuel Hebey,et al. Nonlinear analysis on manifolds , 1999 .
[10] GinéM Evarist,et al. The addition formula for the eigenfunctions of the Laplacian , 1975 .
[11] Hrushikesh Narhar Mhaskar,et al. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature , 2001, Math. Comput..
[12] E. Saff,et al. Distributing many points on a sphere , 1997 .
[13] E. Saff,et al. Discretizing Manifolds via Minimum Energy Points , 2004 .
[14] Christian Hüttig,et al. The spiral grid: A new approach to discretize the sphere and its application to mantle convection , 2008 .
[15] Erik Lehto,et al. A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere , 2012, J. Comput. Phys..
[16] Stefan Kunis,et al. On the computation of nonnegative quadrature weights on the sphere , 2009 .
[17] G. Wright,et al. A hybrid radial basis function–pseudospectral method for thermal convection in a 3‐D spherical shell , 2010 .
[18] Roland Klees,et al. The spherical Slepian basis as a means to obtain spectral consistency between mean sea level and the geoid , 2012, Journal of Geodesy.
[19] Holger Wendland,et al. Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions , 2007, Found. Comput. Math..
[20] I. G. MacDonald,et al. Lectures on Lie groups and Lie algebras , 1995 .
[21] Feng Dai,et al. Approximation of smooth functions on compact two-point homogeneous spaces , 2005, math/0510007.
[22] A. C. Faul,et al. Proof of convergence of an iterative technique for thin plate spline interpolation in two dimensions , 1999, Adv. Comput. Math..
[23] R. Swinbank,et al. Fibonacci grids: A novel approach to global modelling , 2006 .
[24] Natasha Flyer,et al. A radial basis function method for the shallow water equations on a sphere , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[25] T. Hangelbroek,et al. Kernel Approximation on Manifolds II: The L∞ Norm of the L2 Projector , 2010, SIAM J. Math. Anal..
[26] D. Potts,et al. Sampling Sets and Quadrature Formulae on the Rotation Group , 2009 .
[27] Thierry Aubin,et al. Nonlinear analysis on manifolds, Monge-Ampère equations , 1982 .
[28] K. Atkinson,et al. Spherical Harmonics and Approximations on the Unit Sphere: An Introduction , 2012 .
[29] S. Helgason. Groups and geometric analysis , 1984 .
[30] Pencho Petrushev,et al. Localized Tight Frames on Spheres , 2006, SIAM J. Math. Anal..
[31] Hrushikesh Narhar Mhaskar,et al. A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel , 2010 .
[32] Dominik Schmid,et al. Surface Spline Approximation on SO(3) , 2009, 0911.1836.
[33] Stefan Kunis,et al. Fast Summation of Radial Functions on the Sphere , 2006, Computing.
[34] Emmanuel Hebey,et al. Sobolev Spaces on Riemannian Manifolds , 1996 .
[35] J. Hannay,et al. Fibonacci numerical integration on a sphere , 2004 .
[36] Robert E. Mahony,et al. Optimization Algorithms on Matrix Manifolds , 2007 .
[37] Willi Freeden,et al. Handbook of geomathematics , 2010 .
[38] Michael Buchhold,et al. The Operational Global Icosahedral-Hexagonal Gridpoint Model GME: Description and High-Resolution Tests , 2002 .
[39] Robert Michael Kirby,et al. A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method , 2012, Applied numerical mathematics : transactions of IMACS.
[40] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .
[41] Kendall Atkinson,et al. Numerical integration on the sphere , 1982, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.
[42] Alvise Sommariva,et al. INTEGRATION BY RBF OVER THE SPHERE , 2005 .
[43] Holger Wendland,et al. Scattered Data Approximation: Conditionally positive definite functions , 2004 .
[44] Isaac Z. Pesenson,et al. Cubature formulas and discrete fourier transform on compact manifolds , 2011, ArXiv.
[45] Todd D. Ringler,et al. Modeling the Atmospheric General Circulation Using a Spherical Geodesic Grid: A New Class of Dynamical Cores , 2000 .
[46] Álvaro González. Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices , 2009, 0912.4540.
[47] Edward B. Saff,et al. Low Complexity Methods For Discretizing Manifolds Via Riesz Energy Minimization , 2013, Found. Comput. Math..
[48] Manuel Gräf,et al. A unified approach to scattered data approximation on $\mathbb{S}^{\bf 3}$ and SO(3) , 2012, Adv. Comput. Math..
[49] Joseph D. Ward,et al. Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant , 2009, SIAM J. Math. Anal..
[50] F. W. Warner. Foundations of Differentiable Manifolds and Lie Groups , 1971 .
[51] Sigurdur Helgason,et al. Invariant differential operators , 2000 .
[52] G. R. Stuhne,et al. New icosahedral grid-point discretization of the shallow water equation on the sphere , 1999 .