Monomial cubature rules since ``Stroud'': A compilation
type: Item
instance of: scholarly article
title: Monomial cubature rules since ``Stroud'': A compilation
zbMATH Open document ID: 0799.65027
DOI: 10.1016/0377-0427(93)90027-9
author: Ronald Cools
author: Philip Rabinowitz
published in: Journal of Computational and Applied Mathematics
publication date: 1994-11-17T00:00:00Z
review text: This is an important compilation of results and references augmenting and updating those of the classic book ``Approximate calculation of multiple integrals'' by \textit{A. H. Stroud} (1971; Zbl 0379.65013). Regions treated are the \(n\)-cube, the \(n\)-sphere and \(\mathbb{R}^ n\) with radial weight functions. It aims to be comprehensive within the Western literature including translations from outside it. The main results are presented in tabular form with references to an alphabetically ordered bibliography. This form of presentation makes it clear at a glance what results are known, or sometimes some importantly, which results are not known.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65-00
zbMATH DE Number: 540487
zbMATH Keywords: monomial cubature rules
zbMATH Keywords: compilation
zbMATH Keywords: bibliography
Wikidata QID: Q57779011
reviewed by: William E. Smith
describes a project that uses: CUBTRI
MaRDI profile type: Publication
full work available at URL: 0377-0427(93)90027-9
OpenAlex ID: W2076362839
cites work: Q3752861
cites work: On the Construction of Higher Degree Three-Dimensional Embedded Integration Rules
cites work: Numerical integration III. Proceedings of the conference held at the Mathematisches Forschungsinstitut, Oberwolfach, FRG, Nov. 8-14, 1987
cites work: Construction of fully symmetric cubature formulae of degree 4k-3 for fully symmetric planar regions
cites work: Q4725604
cites work: Another step forward in searching for cubature formulae with a minimal number of knots for the square
cites work: Q3796619
cites work: An embedded pair of cubature formulae of degree 5 and 7 for the triangle
cites work: On the construction of multi-dimensional embedded cubature formulae
cites work: Gaussian quadrature formulas for triangles
cites work: Q3323133
cites work: New Euler-Maclaurin Expansions and Their Application to Quadrature Over the s-Dimensional Simplex
cites work: Cubature formulas of the seventh order of accuracy for a hypersphere and a hypercube
cites work: Cubature rules with equal coefficients for integrating functions with respect to symmetric domains
cites work: High degree efficient symmetrical Gaussian quadrature rules for the triangle
cites work: Economical symmetrical quadrature rules for complete polynomials over a square domain
cites work: Efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube
cites work: Q5588056
cites work: Q5603584
cites work: Q3875198
cites work: On the Construction of Good Fully Symmetric Integration Rules
cites work: Q4002712
cites work: Obtaining Cubatures for Rectangles and Other Planar Regions by Using Orthogonal Polynomials
cites work: Orthogonal Polynomials and Approximate Multiple Integration
cites work: The construction of symmetric cubature formulas for the square and the triangle
cites work: Q4011821
cites work: Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region
cites work: An Imbedded Family of Fully Symmetric Numerical Integration Rules
cites work: Invariant Integration Formulas for the n-Simplex by Combinatorial Methods
cites work: Zweidimensionale Quadraturformeln vom Grad 7 mit 14 Punkten
cites work: Circularly symmetrical integration formulas for two-dimensional circularly symmetrical regions
cites work: Q3949460
cites work: Q4725603
cites work: Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials
cites work: Construction of Cubature Formulas of Degree Seven and Nine Symmetric Planar Regions, Using Orthogonal Polynomials
cites work: Q5678364
cites work: Numerical integration on a triangle
cites work: Numerical integration on a tetrahedron
cites work: Quadrature Formulas over Fully Symmetric Planar Regions
cites work: Cubatures of Precision 2k and 2k + 1 for Hyperrectangles
cites work: Symmetric Gaussian quadrature formulae for tetrahedronal regions
cites work: Some Fully Symmetric Quadrature Formulae for Product Spaces
cites work: Moderate-degree tetrahedral quadrature formulas
cites work: Q3751535
cites work: Q4153998
cites work: Q3490422
cites work: Algorithm 584: CUBTRI: Automatic Cubature over a Triangle
cites work: Some criteria for numerically integrated matrices and quadrature formulas for triangles
cites work: Symmetric integration rules for hypercubes. I. Error coefficients
cites work: Integration Rules of Hypercubic Symmetry Over a Certain Spherically Symmetric Space
cites work: Moderate Degree Symmetric Quadrature Rules for the Triangle
cites work: On Symmetric Cubature Formulae for Planar Regions
cites work: Shortened quadrature rules for finite elements
cites work: The Application of Integer Programming to the Computation of Fully Symmetric Integration Formulas in Two and Three Dimensions
cites work: Experiences with Orthogonal Polynomials and „Best”︁ Numerical Integration Formulas on a Triangle; with Particular Reference to Finite Element Approximations
cites work: Kubaturformeln mit minimaler Knotenzahl

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q3951455

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: The Construction of Algebraic Cubature Formulae by the Distribution of Nodes Along Selected Lines

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q3323132

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q4740960

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Seventh degree integration rules for the cube

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Seventh degree integration rules for the sphere

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Seventh degree integration rules for \(R^ 3\).

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Cubature formulas of degree eleven for symmetric planar regions

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Cubature Formulas of Degree Nine for Symmetric Planar Regions

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q3774289

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q4720663

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: On cubature formulae with a minimal number of knots

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q3322559

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Fully symmetric integration rules for the 4-cube

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q4404383

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Q4158394

Monomial cubature rules since ``Stroud'': A compilation (cites work)
cites work: Partially Symmetric Cubature Formulas for Even Degrees of Exactness

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Monomial cubature rules since ``Stroud'': A compilation. II
Similarity Score: 0.9877611
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: On the computation of Gauss quadrature rules for measures with a monomial denominator
Similarity Score: 0.8435978
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Cubature rules from Hall–Littlewood polynomials
Similarity Score: 0.8419019
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube
Similarity Score: 0.833563
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Q3803601
Similarity Score: 0.8326829
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Q4011820
Similarity Score: 0.8321173
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Simple cubature formulas with high polynomial exactness
Similarity Score: 0.8294303
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Multicriterial problems of the theory of cubature formulas
Similarity Score: 0.8288008
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Best approximation to monomials on a cube
Similarity Score: 0.8277281
Recommender Run: Recommender Run 3

Monomial cubature rules since ``Stroud'': A compilation (Recommended article)
Recommended article: Q3705906
Similarity Score: 0.826635
Recommender Run: Recommender Run 3