Structured Inversion of the Bernstein Mass Matrix

DOI10.1137/19M1284166zbMath1441.65043arXiv1907.05773OpenAlexW3016412360MaRDI QIDQ5112236

Robert C. Kirby, Larry Allen

Publication date: 28 May 2020

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05773

zbMATH Keywords

Bernstein polynomialsconditioningspectral decompositionfast algorithmLegendre polynomialsBézout matrixmatrix inverseBernstein mass matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Preconditioners for iterative methods (65F08)

Related Items

Bounds-constrained polynomial approximation using the Bernstein basis ⋮ Total positivity and accurate computations with Gram matrices of Bernstein bases ⋮ On the accuracy of de Casteljau-type algorithms and Bernstein representations ⋮ Structured Inversion of the Bernstein--Vandermonde Matrix ⋮ Recursive, Parameter-Free, Explicitly Defined Interpolation Nodes for Simplices

Uses Software

• Chebfun

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bézier representation of the constrained dual Bernstein polynomials
• Fast simplicial quadrature-based finite element operators using Bernstein polynomials
• Gram matrix of Bernstein basis: properties and applications
• Fast inversion of the simplicial Bernstein mass matrix
• Geometric decompositions and local bases for spaces of finite element differential forms
• Algebraic methods for Toeplitz-like matrices and operators
• Legendre-Bernstein basis transformations
• A fast eigenvalue algorithm for Hankel matrices
• Bernstein-Bézier bases for tetrahedral finite elements
• An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing
• Fast simplicial finite element algorithms using Bernstein polynomials
• Low-Complexity Finite Element Algorithms for the de Rham Complex on Simplices
• Preconditioning discretizations of systems of partial differential equations
• Chebfun: A New Kind of Numerical Computing
• Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
• From Functional Analysis to Iterative Methods
• Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex