A Computational Procedure for the Approximation of Random Functions.
A Contribution to the Theory of Condition.
A Dual Algorithm for Convex-Concave Data Smoothing by Cubic C2-Splines.
A Fast ' Monte-Carlo Cross-Validation' Procedure for Large Least Squares Problems with Noisy Data.
A full-Newton approach to separable nonlinear least squares problems and its application to discrete least squares rational approximation.
A Least Squares Method for Finding the Preisach Hysteresis Operator from Measurements.
A new curve fitting based rating prediction algorithm for recommender systems
The most algorithms for Recommender Systems (RSs) are based on a Collaborative Filtering (CF) approach, in particular on the Probabilistic Matrix Factorization (PMF) method. It is known that the PMF method is quite successful for the rating prediction. In this study, we consider the problem of rating prediction in RSs. We propose a new algorithm which is also in the CF framework; however, it is completely different from the PMF-based algorithms. There are studies in the literature that can increase...
A note on Newbery's algorithm for discrete least-squares approximation by trigonometric polynomials.
A Note on Polynomial Splines with Free Knots.
A numerical method of fitting a multiparameter nonlinear function to experimental data in the norm
A numerical method of fitting a multiparameter function, non-linear in the parameters which are to be estimated, to the experimental data in the norm (i.e., by minimizing the sum of absolute values of errors of the experimental data) has been developed. This method starts with the least squares solution for the function and then minimizes the expression , where is the error of the -th experimental datum, starting with an comparable with the root-mean-square error of the least squares solution...
Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process
A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.
Acceleration of Le Bail fitting method on parallel platforms
Le Bail fitting method is procedure used in the applied crystallography mainly during the crystal structure determination. As in many other applications, there is a need for a great performance and short execution time. In this paper, we describe utilization of parallel computing for mathematical operations used in Le Bail fitting. We present an algorithm implementing this method with highlighted possible approaches to its aforementioned parallelization. Then, we propose a sample parallel version...
Algorithms. 49. PIECE LIN REGR. An algorithm for fitting discontinuous multiphase linear least-square regression
Almost curvature continuous fitting of B-spline surfaces.
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An algorithm for the approximation by cubic splines
An approximate necessary condition for the optimal bandwidth selector in kernel density estimation
An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.
An approximation of tabulated function.
An Efficient Method for Calculating Smoothing Splines Using Orthogonal Transformations.
Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting
This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in . A family of fully discrete approximation...