Bivariate quadratic simplicial B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a Cl-smooth surface. The generation of triangle vertices is adjusted to the area1 distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-s...

Time series associated with single-molecule experiments and/or simulations contain a wealth of multiscale information about complex biomolecular systems. We demonstrate how a collection of Penalized-splines (P-splines) can be useful in quantitatively summarizing such data. In this work, functions estimated using P-splines are associated with stochastic differential equations (SDEs). It is shown...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the...

Splines and multiresolution are two independent concepts, which – considered together – yield a vast variety of bases for image processing and image analysis. The idea of a multiresolution analysis is to construct a ladder of nested spaces that operate as some sort of mathematical looking glass. It allows to separate coarse parts in a signal or in an image from the details of various sizes. Spl...

We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of quadratic-like splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the Boolean sum of univariate B-splines and show that for a proper choice of the degrees, the splines...

We consider a space of Chebyshev splines whose left and right derivatives satisfy linear constraints that are given by arbitrary non-singular connection matrices. We show that for almost all knot sequences such spline spaces have basis functions whose support is equal to the support of the ordinary B-splines with the same knots. Consequently, there are knot insertion and evaluation algorithms a...

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of surface is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is estab...

• We study the problem of estimating smooth curves which verify structural properties. propose a mathematical optimization formulation to build constrained P-splines. An open-source Python library is developed: cpsplines. estimate in simulated, COVID-19 and demographic data. Decision-making often based on analysis complex evolving Thus, having systems allow incorporate human knowledge provide v...

A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a Gramian, is obtained efficiently orthogonalize the B-splines. The can be also used fast inversion method Gramian characterized by remarkable sparsity of matrix. There are two versions algorithm: first one more efficient and applicable Toeplitz while second general, works with any but computationall...

Non parametric regression methods can be presented in two main clusters. The one of smoothing splines methods requiring positive kernels and the other one known as Nonparametric Kernel Regression allowing the use of non positive kernels such as the Epanechnikov kernel. We propose a generalization of the smoothing spline method to include kernels which are still symmetric but not positive semi d...