Related papers: Cubic-matrix splines and second-order matrix model…
Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximation theory and numerical analysis, with applications in data…
Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…
The extended definition of the polynomial B-splines may give a chance to improve the results obtained by the classical cubic polynomial B-splines. Determination of the optimum value of the extension parameter can be achieved by scanning…
Explicit pointwise error bounds for the interpolation of a smooth function by piecewise exponential splines of order four are given. Estimates known for cubic splines are extended to a natural class of piecewise exponential splines which…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
This paper proposes a specific type of Local Linear Model, the Shuffled Linear Model (SLM), that can be used as a universal approximator. Local operating points are chosen randomly and linear models are used to approximate a function or…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky equation. Having only first and second order derivatives of the…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
This work presents a novel algorithm for transforming a neural network into a spline representation. Unlike previous work that required convex and piecewise-affine network operators to create a max-affine spline alternate form, this work…