A fast and accurate algorithm for solving Bernstein-Vandermonde linear systems
From MaRDI portal
Publication:875013
DOI10.1016/j.laa.2006.11.020zbMath1116.65038arXivmath/0605577OpenAlexW2054956151MaRDI QIDQ875013
Ana Marco, José-Javier Martıńez
Publication date: 10 April 2007
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0605577
algorithmVandermonde matrixInterpolationBernstein basisbidiagonal factorizationTotal positivityBidiagonal decompositionHigh relative accuracy
Related Items
Rectifying control polygon for planar Pythagorean hodograph curves, Linearizations of matrix polynomials in Bernstein bases, Fast and accurate algorithms for Jacobi-Stirling matrices, Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases, Total Positivity: A New Inequality and Related Classes of Matrices, Accurate computations with matrices related to bases \(\{t^ie^{\lambda t}\}\), Accurate computations with collocation matrices of the Lupaş-type \((p,q)\)-analogue of the Bernstein basis, Tests for the recognition of total positivity, Accurate computations of matrices with bidiagonal decomposition using methods for totally positive matrices, Preconditioned progressive iterative approximation for tensor product Bézier patches, Richardson method and totally nonnegative linear systems, Accurate polynomial interpolation by using the Bernstein basis, Bernstein-Bezoutian matrices and curve implicitization, Accurate computation of eigenvalues of generalized sign regular quasi-Said-Ball-Vandermonde matrices, Accurate and fast computations with positive extended Schoenmakers-Coffey matrices, Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank, Accurate and fast computations with Green matrices, Extremal and optimal properties of B-bases collocation matrices, The Bernstein polynomial basis: a centennial retrospective, Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices, Accurate singular values of a class of parameterized negative matrices, Accurate computations with Lupaş matrices, Accurate Computations and Applications of Some Classes of Matrices, On the formulation of a BEM in the Bézier-Bernstein space for the solution of Helmholtz equation, GPU-Accelerated Bernstein--Bézier Discontinuous Galerkin Methods for Wave Problems, Accurate computations with Said-Ball-Vandermonde matrices, Deformation of spatial septic Pythagorean hodograph curves using Gauss-Legendre polygon, Gauss-Lobatto polygon of Pythagorean hodograph curves, Accurate bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices and applications, Accurate solutions of weighted least squares problems associated with rank-structured matrices, Accurate solutions of structured generalized Kronecker product linear systems, Polynomial least squares fitting in the Bernstein basis, Similarity to totally positive matrices and accurate computations, Accurate computations with Wronskian matrices, New shape control tools for rational Bézier curve design, Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis, Progressive iterative approximation for extended cubic uniform B-splines with shape parameters, Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension, Flip procedure in geometric approximation of multiple-component shapes – Application to multiple-inclusion detection, A note on Bernstein-Vandermonde matrices, Accurate algorithms for Bessel matrices, Structured Inversion of the Bernstein--Vandermonde Matrix, A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy, Least squares problems involving generalized Kronecker products and application to bivariate polynomial regression, Preconditioned progressive iterative approximation for triangular Bézier patches and its application, Optimal interval length for the collocation of the Newton interpolation basis, Matrices with Bidiagonal Decomposition, Accurate Computations and Corner Cutting Algorithms, Accurate Computations with Collocation Matrices of q-Bernstein Polynomials, Accurate Computation of Generalized Eigenvalues of Regular SR-BP Pairs, Algorithm 960
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bernstein-Bézoutian matrices
- Backward error analysis of Neville elimination
- Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems
- Algorithms for polynomials in Bernstein form
- Factorizations of Cauchy-Vandermonde matrices
- Total positivity and Neville elimination
- A matricial description of Neville elimination with applications to total positivity
- Shape preserving representations and optimality of the Bernstein basis
- A fast parallel Björck-Pereyra-type algorithm for solving Cauchy linear equations
- On the stability of transformations between power and Bernstein polynomial forms
- Effectively Well-Conditioned Linear Systems
- Accuracy and Stability of Numerical Algorithms
- Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
- The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System
- Solution of Vandermonde systems of equations
