Spline-Fourier Approximations of Discontinuous Waves.

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel integral equation. These results are derived by developing a Fourier representation for a smoothing spline.

Smoothing

Spline (mechanical)

Kernel (algebra)

Polyharmonic spline

10.1214/aos/1176346065

Cite

Citations (154)

Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates

ISRN Mathematical Analysis (2012)

R. K. Mohanty Rajive Kumar Vijay Dahiya

Using nonpolynomial cubic spline approximation in x- and finite difference in y-direction, we discuss a numerical approximation of O(k2+h4) for the solutions of diffusion-convection equation, where k>0 and h>0 are grid sizes in y- and x-coordinates, respectively. We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates. Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.

10.5402/2012/234516

Cite

Citations (2)

Discontinuity localization and spline approximation of discontinuous functions with many variables at scattered meshes

Russian Journal of Numerical Analysis and Mathematical Modelling (1990)

Vladimír A. Vasilenko Alexander B. Rozhenko

Discontinuity (linguistics)

Spline (mechanical)

10.1515/rnam.1990.5.4-5.425

Cite

Citations (0)

An accurate cubic-spline boundary-integral formulation for two-dimensional free-surface flow problems

Springer eBooks (2008)

Debabrata Sen

Monotone cubic interpolation

Free surface

10.1007/3-540-59280-6_125

Cite

Citations (2)

Spline Finite Point Method for Geometrically Nonlinear Analysis of Arch Structure

Journal of Southwest Jiaotong University (2000)

Duan Hai

A spline finite point method for geometrically nonlinear analysis of arch structure is presented. With the displacement components u and w treated as fundamental unknown variables, and the cubic B spline functions as displacement functions, the nonlinear stiffness equations of spline discretization are established based on the principle of minimum potential energy, and the precise explicit expression of the nonlinear tangential stiffness matrix is derived.

Spline (mechanical)

B-spline

Source

Cite

Citations (0)

Trigonometric B-Spline Collocation Algorithm for Solving the Rlw Equation

İdris Dağ Dursun Irk O. Kaçmaz Nihat Adar

Collocation (remote sensing)

B-spline

Spline (mechanical)

Source

Cite