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The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…
This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by using regularized delta functions derived from composite B-splines. The conventional IB method, while effective for fluid-structure…
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 apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…
Interpolation and internal painting are one of the basic approaches in image internal painting, which is used to eliminate undesirable parts that occur in digital images or to enhance faulty parts. This study was designed to compare the…
The main result in this paper is an error estimate for interpolation biharmonic polysplines in an annulus $A\left( r_{1},r_{N}\right) $, with respect to a partition by concentric annular domains $A\left( r_{1} ,r_{2}\right) ,$ ....,…
A realistic generalization of the Markov--Dubins problem, which is concerned with finding the shortest planar curve of constrained curvature joining two points with prescribed tangents, is the requirement that the curve passes through a…
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which…
Radio-frequency pulses are widespread for the control of quantum bits and the execution of operations in quantum computers. The ability to tune key pulse parameters such as time-dependent amplitude, phase, and frequency is essential to…
Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
In experimental control of quantum systems, the precision is often hindered by imperfect applied electronics that distort control pulses delivered to target quantum devices. To mitigate such error, the deconvolution method is commonly used…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
Ultrasound poroelastography is a cost-effective non-invasive imaging technique, which is able to reconstruct several mechanical parameters of cancer and normal tissue such as Young's modulus, Poisson's ratio, interstitial permeability and…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…