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2017 Workshop on Spline Approximation and its Applications
2017 Workshop Spline Approximation and its Applications
2017/11/24
Spline functions are polynomials that are cut into pieces with care. Although spline functions date back to work of Euler and Bernoulli, it was Iso Schoenberg who began to study them in earnest. In la...
ADAPTIVE SPLINE ESTIMATES FOR NONPARAMETRIC REGRESSION MODELS
ADAPTIVE SPLINE ESTIMATES NONPARAMETRIC REGRESSION MODELS
2015/8/25
ADAPTIVE SPLINE ESTIMATES FOR NONPARAMETRIC REGRESSION MODELS.
Cubic Spline Trajectory Generation with Axis Jerk and Tracking Error Constraints
Cubic spline trajectory conned jerk PID controller tracking error minimum time
2013/9/9
This paper presents a cubic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration proˉles for 3-axis CNC machines with conˉned axis jerk and tracking err...
A Cubic Spline Method for Solving a Unilateral Obstacle Problem
Obstacle Problem Spline Collocation Nonsmooth Equation Generalized Newton Method
2012/9/30
This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically ...
Flexible Multi-scale Image Alignment Using B-Spline Reparametrization -Theoretical Analysis
Flexible alignment L2-gradient flow Bi-cubic B-spline Existence and uniqueness System of ordinary differential equations
2012/8/10
In the first part of this companion volumes, we present a new flexible alignment model and
an iterative algorithm based on an L2-gradient flow. In this second part of the companion
volumes, we focus...
Flexible Multi-scale Alignment Using B-Spline Reparameterization-Computational Methods
Flexible Alignment L2-gradient flow Bi-cubic B-spline Finite elementmethod Multi-resolution representation
2012/8/10
In this first part of the companion volumes, we present a new flexible alignment method
to align two or more similar images, especially biological images. By minimizing an energy
functional measurin...
Solving Two-Point Boundary Value Problems of Fractional Differential Equations by Spline Collocation Methods
Caputo抯 derivatives Collocation methods Cubic spline functions Riemann-Liouvillefractional derivative
2012/8/10
We use collocation methods to solve fractional boundary value problems. Analytically, we study the
existence and uniquenes theorem of the collocation solutions, and discuss some error estimates. We
...
G1 B-Spline Surface Construction By Geometric Partial Differential Equations
B-Spline surface discretizations geometric PDE Convergence
2012/8/8
In this paper, we propose a dynamic B-spline technique using general form fourth order geometric
PDEs. Basing on discretizaions of Laplace-Beltrami operator and Gaussian curvature over triangular
an...
G1 Spline Surface Construction By Geometric Partial Differential Equations Using Mixed Finite Element Methods
Spline surface Discretizations GPDE Convergence
2012/8/8
Variational formulations of three fourth order geometric partial di甧rential equations are
derived, and based on which mixed 痭ite element methods are presented for constructing
G1 smooth B-spline sur...
Regularization of B-Spline Objects
Spline objects Regularization L2-gradient Finite element method
2012/8/8
By a d-dimensional B-spline object (denoted as Od), we mean a B-spline curve (d = 1), a
B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object
Od we mean a pro...
A study of the uniform accuracy of univariate thin plate spline interpolation
plate spline interpolation Numerical Analysis
2011/7/21
Abstract: The usual power function error estimates do not capture the true order of uniform accuracy for thin plate spline interpolation to smooth data functions in one variable. In this paper we prop...
Numerical Solution of Obstacle Problems by B-Spline Functions
Least Square Method Uniform B-Splines Boundary Value Problems Obstacle Problems
2011/6/30
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The pro...
An O(k2+kh2+h2) Accurate Two-level Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations
Quasi-Linear Parabolic Equation, Implicit Method, Cubic Spline Approximation, Diffusion-Convection Equation, Singular Equation, Burgers’ Equation, Reynolds Number
2011/3/30
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0< x <1, t > 0...
We consider numerical approximations of the Monge-Ampere equation det D2u = f; f > 0 with Dirichlet boundary conditions on a convex bounded domain in Rn; n = 2; 3. We make a comparative study of thr...
On the dimension of spline spaces on planar T-subdivisions
spline spaces planar T-subdivisions
2010/11/1
We analyze the space S_{m, m'}^{r, r'} (T) of bivariate functions that are piecewise polynomial of bidegree (m, m') and class C^{r, r'} over a planar T-subdivision. We give a new formula for the dime...