$H^2$-Convergence of Least-Squares Kernel Collocation Methods
نویسندگان
چکیده
منابع مشابه
H2-Convergence of Least-Squares Kernel Collocation Methods
The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems and partial differential equations despite the lack of theoretical support. The simple leastsquares (LS) formulation, on the other hand, makes the study of its solvability and convergence rather nontrivial. In this p...
متن کاملConvergence analyses of Galerkin least - squares methods
Symmetric advective-di usive forms of the Stokes and incompressible Navier-Stokes equations are presented. The Galerkin least-squares method for advective-di usive equations is used for both systems and is related to other stabilized methods previously studied. The presentation reveals that the convergence analysis for advective-di usive equations, as applied before to a linearized form of the ...
متن کاملA least-squares preconditioner for radial basis functions collocation methods
Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring O...
متن کاملConvergence of Unsymmetric Kernel-Based Meshless Collocation Methods
This paper proves convergence of variations of the unsymmetric kernel-based collocation method introduced by E. Kansa in 1986. Since then, this method has been very successfully used in many applications, though it may theoretically fail in special situations, and though it had no error bound or convergence proof up to now. Thus it is necessary to add assumptions or to make modifications. Our m...
متن کاملKernel Recursive Least Squares
We present a non-linear kernel-based version of the Recursive Least Squares (RLS) algorithm. Our Kernel-RLS algorithm performs linear regression in the feature space induced by a Mercer kernel, and can therefore be used to recursively construct the minimum meansquared-error regressor. Sparsity (and therefore regularization) of the solution is achieved by an explicit greedy sparsification proces...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2018
ISSN: 0036-1429,1095-7170
DOI: 10.1137/16m1072863