We present an overlapping domain decomposition technique for solving the LaplaceBeltrami equation on the sphere with spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O (H/h), where H and h are the sizes of the coarse and fine meshes, respectively. In the case that the degree of the splines is even, a better bound O (max1≤k≤J (1 +Hk/δk)) is pro...

EEG/MEG source localization based on a "distributed solution" is severely underdetermined, because the number of sources is much larger than the number of measurements. In particular, this makes the solution strongly affected by sensor noise. A new way to constrain the problem is presented. By using the anatomical basis of spherical harmonics (or spherical splines) instead of single dipoles the...

EEG/MEG source localization based on minimum-norm estimate is hindered by the two problems: the localization is non-unique (since the number of sources is much larger than the number of signals) and unstable (the solution is highly sensitive to sensor noise). A new source localization algorithm is presented, which addresses both problems in a simple manner. By using the neural basis of spherica...

in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

In this paper, we implement and compare the accuracy of ordinary kriging, lognormal ordinary kriging, inverse distance weighting (IDW) and splines for interpolating seasonally stable soil properties (pH, electric conductivity and organic matter) that have been demonstrated to affect yield production. The choice of the exponent value for IDW and splines as well as the number of the closest neigh...

This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type difference penalty with B-splines (HB-splines), were recently introduced the authors as generalization P-splines. HB-splines are bell-shaped basis functions consisting segments made real exponentials eαx,e−αx and linear mu...

‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis ...