Matches in SemOpenAlex for { <https://semopenalex.org/work/W2002600311> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2002600311 endingPage "21" @default.
- W2002600311 startingPage "5" @default.
- W2002600311 abstract "One of the integration methods of the equality type is Gauss-Chebyshev quadrature rule, which is in the following form:@!-11f(x)1-x^2dx=@pn@?k=1nfcos(2k-1)@p2n+2@p2^2^n(2n)!f^(^2^n^)(@h),-1<@h<1.According to Gauss quadrature rules, the precision degree of above formula is the highest, i.e. 2n-1. Hence, it is not possible to increase the precision degree of Gauss-Chebyshev integration formulas anymore. In this way, we present a matrix proof for this matter. But, on the other hand, we claim that we can improve the above formula numerically. To do this, we consider the integral bounds as two unknown variables. This causes to numerically be extended the monomial space f(x)=x^j from j=0,1,...,2n-1 to j=0,1,...,2n+1. This means that we have two monomials more than Gauss-Chebyshev integration method. In other words, we give an approximate formula as:@!abf(x)1-x^2dx~@?i=1nwif(xi),in which a,b and w1,w2,...,wn and x1,x2,...,xn are all unknowns and the formula is almost exact for the monomial basis f(x)=x^j, j=0,1,...,2n+1. Some important examples are finally given to show the excellent superiority of the proposed nodes and weights with respect to the usual Gauss-Chebyshev nodes and weights. Let us add that in this part we have also some wonderful 2-point formulas that are comparable with 71-point formulas of Gauss-Chebyshev quadrature rules in average." @default.
- W2002600311 created "2016-06-24" @default.
- W2002600311 creator A5001778077 @default.
- W2002600311 creator A5023884718 @default.
- W2002600311 creator A5044309986 @default.
- W2002600311 date "2005-06-01" @default.
- W2002600311 modified "2023-10-17" @default.
- W2002600311 title "On numerical improvement of the first kind Gauss–Chebyshev quadrature rules" @default.
- W2002600311 cites W1987077436 @default.
- W2002600311 cites W1997520325 @default.
- W2002600311 cites W2005876858 @default.
- W2002600311 cites W2008829362 @default.
- W2002600311 cites W2020328455 @default.
- W2002600311 cites W2059654265 @default.
- W2002600311 doi "https://doi.org/10.1016/j.amc.2004.06.102" @default.
- W2002600311 hasPublicationYear "2005" @default.
- W2002600311 type Work @default.
- W2002600311 sameAs 2002600311 @default.
- W2002600311 citedByCount "19" @default.
- W2002600311 countsByYear W20026003112012 @default.
- W2002600311 countsByYear W20026003112013 @default.
- W2002600311 countsByYear W20026003112020 @default.
- W2002600311 countsByYear W20026003112022 @default.
- W2002600311 crossrefType "journal-article" @default.
- W2002600311 hasAuthorship W2002600311A5001778077 @default.
- W2002600311 hasAuthorship W2002600311A5023884718 @default.
- W2002600311 hasAuthorship W2002600311A5044309986 @default.
- W2002600311 hasConcept C10628310 @default.
- W2002600311 hasConcept C120665830 @default.
- W2002600311 hasConcept C121332964 @default.
- W2002600311 hasConcept C122107654 @default.
- W2002600311 hasConcept C127349201 @default.
- W2002600311 hasConcept C129785596 @default.
- W2002600311 hasConcept C134306372 @default.
- W2002600311 hasConcept C14103991 @default.
- W2002600311 hasConcept C142484921 @default.
- W2002600311 hasConcept C161794534 @default.
- W2002600311 hasConcept C162046254 @default.
- W2002600311 hasConcept C167196314 @default.
- W2002600311 hasConcept C172657837 @default.
- W2002600311 hasConcept C199343813 @default.
- W2002600311 hasConcept C21424316 @default.
- W2002600311 hasConcept C21736991 @default.
- W2002600311 hasConcept C27016315 @default.
- W2002600311 hasConcept C2777686260 @default.
- W2002600311 hasConcept C28826006 @default.
- W2002600311 hasConcept C33923547 @default.
- W2002600311 hasConcept C48265008 @default.
- W2002600311 hasConcept C48753275 @default.
- W2002600311 hasConcept C54691486 @default.
- W2002600311 hasConcept C62520636 @default.
- W2002600311 hasConcept C62869609 @default.
- W2002600311 hasConcept C71924100 @default.
- W2002600311 hasConceptScore W2002600311C10628310 @default.
- W2002600311 hasConceptScore W2002600311C120665830 @default.
- W2002600311 hasConceptScore W2002600311C121332964 @default.
- W2002600311 hasConceptScore W2002600311C122107654 @default.
- W2002600311 hasConceptScore W2002600311C127349201 @default.
- W2002600311 hasConceptScore W2002600311C129785596 @default.
- W2002600311 hasConceptScore W2002600311C134306372 @default.
- W2002600311 hasConceptScore W2002600311C14103991 @default.
- W2002600311 hasConceptScore W2002600311C142484921 @default.
- W2002600311 hasConceptScore W2002600311C161794534 @default.
- W2002600311 hasConceptScore W2002600311C162046254 @default.
- W2002600311 hasConceptScore W2002600311C167196314 @default.
- W2002600311 hasConceptScore W2002600311C172657837 @default.
- W2002600311 hasConceptScore W2002600311C199343813 @default.
- W2002600311 hasConceptScore W2002600311C21424316 @default.
- W2002600311 hasConceptScore W2002600311C21736991 @default.
- W2002600311 hasConceptScore W2002600311C27016315 @default.
- W2002600311 hasConceptScore W2002600311C2777686260 @default.
- W2002600311 hasConceptScore W2002600311C28826006 @default.
- W2002600311 hasConceptScore W2002600311C33923547 @default.
- W2002600311 hasConceptScore W2002600311C48265008 @default.
- W2002600311 hasConceptScore W2002600311C48753275 @default.
- W2002600311 hasConceptScore W2002600311C54691486 @default.
- W2002600311 hasConceptScore W2002600311C62520636 @default.
- W2002600311 hasConceptScore W2002600311C62869609 @default.
- W2002600311 hasConceptScore W2002600311C71924100 @default.
- W2002600311 hasIssue "1" @default.
- W2002600311 hasLocation W20026003111 @default.
- W2002600311 hasOpenAccess W2002600311 @default.
- W2002600311 hasPrimaryLocation W20026003111 @default.
- W2002600311 hasRelatedWork W1976833400 @default.
- W2002600311 hasRelatedWork W2002600311 @default.
- W2002600311 hasRelatedWork W2004896651 @default.
- W2002600311 hasRelatedWork W2006936197 @default.
- W2002600311 hasRelatedWork W2041338518 @default.
- W2002600311 hasRelatedWork W2055370439 @default.
- W2002600311 hasRelatedWork W2062078770 @default.
- W2002600311 hasRelatedWork W2258903751 @default.
- W2002600311 hasRelatedWork W2766994706 @default.
- W2002600311 hasRelatedWork W4300584626 @default.
- W2002600311 hasVolume "165" @default.
- W2002600311 isParatext "false" @default.
- W2002600311 isRetracted "false" @default.
- W2002600311 magId "2002600311" @default.
- W2002600311 workType "article" @default.