On the optimal stability of the Bernstein basis
From MaRDI portal
Publication:4718406
DOI10.1090/S0025-5718-96-00759-4zbMath0853.65051OpenAlexW2005799419MaRDI QIDQ4718406
Tim N. T. Goodman, Rida T. Farouki
Publication date: 3 December 1996
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-96-00759-4
interval arithmeticcomparisonsBernstein polynomial basisoptimal stabilitygeneralized Ball basespower basesnonnegative basis transformations
Computer-aided design (modeling of curves and surfaces) (65D17) Error analysis and interval analysis (65G99)
Related Items
Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bézier curves, High-order quadrature on multi-component domains implicitly defined by multivariate polynomials, Robust plotting of generalized lemniscates, A rational cubic clipping method for computing real roots of a polynomial, Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces, Numerical solution of various cases of Cauchy type singular integral equation, Numerical solution of linear integral equations system using the Bernstein collocation method, The uniqueness of the rational Bézier polygon is unique, Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains, Linear perturbation methods for topologically consistent representations of free-form surface intersections, Topologically consistent trimmed surface approximations based on triangular patches, Recursive de Casteljau bisection and rounding errors, A structure-preserving matrix method for the deconvolution of two Bernstein basis polynomials, Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm, Computing the roots of sparse high-degree polynomials that arise from the study of random simplicial complexes, Accurate polynomial interpolation by using the Bernstein basis, Banded operational matrices for Bernstein polynomials and application to the fractional advection-dispersion equation, Total positivity and accurate computations with Gram matrices of Bernstein bases, Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations, Numerical solutions of high-order differential equations with polynomial coefficients using a Bernstein polynomial basis, Multi-objective optimization of snap-through instability of helicoidal composite imperfect beams using Bernstein polynomials method, On the accuracy of de Casteljau-type algorithms and Bernstein representations, Bernstein-Bézier \(H(\mathrm{curl})\)-conforming finite elements for time-harmonic electromagnetic scattering problems, Approximate implicitization using linear algebra, Gauss-Legendre polynomial basis for the shape control of polynomial curves, Numerical solution of distributed-order fractional 2D optimal control problems using the Bernstein polynomials, Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials, Standard and Non-standard CAGD Tools for Isogeometric Analysis: A Tutorial, Bernstein Bézoutians and application to intersection problems, Normalized Bernstein polynomials in solving space-time fractional diffusion equation, Optimal stability of the Lagrange formula and conditioning of the Newton formula, The Bernstein polynomial basis: a centennial retrospective, The transformation of the companion matrix resultant between the power and Bernstein polynomial bases., Strongly stable bases for adaptively refined multilevel spline spaces, Solutions of 2nd-order linear differential equations subject to Dirichlet boundary conditions in a Bernstein polynomial basis, On multivariate polynomials in Bernstein-Bézier form and tensor algebra, Generalized Heine–Stieltjes and Van Vleck polynomials associated with two-level, integrable BCS models, Rational cubic clipping with linear complexity for computing roots of polynomials, B-splines and optimal stability, Exponential Bernstein functions: an effective tool for the solution of heat transfer of a micropolar fluid through a porous medium with radiation, Bernstein operational matrix of fractional derivatives and its applications, A quadratic clipping step with superquadratic convergence for bivariate polynomial systems, An improved rational cubic clipping method for computing real roots of a polynomial, Explicit solution of the finite time \(L_{2}\)-norm polynomial approximation problem, A note on the optimal stability of bases of univariate functions, On the generalized Ball bases, Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis, Bernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equation, A model-based PID controller for Hammerstein systems using B-spline neural networks, Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme, Multiple Degree Reduction and Elevation of Bézier Curves Using Jacobi–Bernstein Basis Transformations, Differentiation matrices for univariate polynomials, On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus, Local hybrid approximation for scattered data fitting with bivariate splines, Computing roots of polynomials by quadratic clipping, On Bernstein type polynomials and their applications, Subdivision methods for solving polynomial equations, The Runge Example for Interpolation and Wilkinson's Examples for Rootfinding, Bernstein operators for exponential polynomials, Legendre-Bernstein basis transformations, Unnamed Item, Evaluation of the derivative of a polynomial in Bernstein form, Monotonicity preservation on triangles, Shape-constrained estimation in functional regression with Bernstein polynomials, Numerical solution of two and three-dimensional fractional heat conduction equations via Bernstein polynomials, A companion matrix resultant for Bernstein polynomials, System identification of Wiener systems with B-spline functions using De Boor recursion, Algorithm 960, Multi-degree reduction of disk Bézier curves with \(G^{0}\)- and \(G^{1}\)-continuity
Uses Software
Cites Work
- Shape preserving properties of the generalised Ball basis
- On the numerical condition of polynomials in Bernstein form
- Properties of generalized Ball curves and surfaces
- Shape preserving representations and optimality of the Bernstein basis
- The evaluation of the zeros of ill-conditioned polynomials. I, II
- A generalized Ball curve and its recursive algorithm
- Unnamed Item
- Unnamed Item
- Unnamed Item
