Matches in SemOpenAlex for { <https://semopenalex.org/work/W2106584246> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W2106584246 abstract "In computational dealings with splines, the question of representation is of primary importance. For splines of fixed order on a fixed partition, this is a question of choice of basis, since such splines form a linear space. Only three kinds of bases for spline spaces have actually been given serious attention; those consisting of truncated power functions, of cardinal splines, and of B-splines. Truncated power bases are known to be open to severe illconditioning, while cardinal splines are difficult to calculate. By contrast, bases consisting of B-splines are well-conditioned, at least for orders < 20. Such bases are also local in the sense that at every point only a fixed number (equal to the order) of B-splines is nonzero. B-splines are also evaluated quite easily, using their definition as a divided difference of the truncated power function. Unfortunately, such calculations are ill-conditioned, particularly for partitions of widely varying interval lengths, as is indicated by the fact that special measures have to be taken in case of coincident knots. In this note, a different way of evaluating B-splines is discussed which is very well conditioned yet efficient, and which needs no special adjustments in case of coincident knots. It is also shown that the condition of the B-spline basis increases exponentially with the order." @default.
- W2106584246 created "2016-06-24" @default.
- W2106584246 creator A5010835041 @default.
- W2106584246 date "1972-01-01" @default.
- W2106584246 modified "2023-09-24" @default.
- W2106584246 title "On Calculating with Mplines" @default.
- W2106584246 cites W2004445558 @default.
- W2106584246 cites W2021813574 @default.
- W2106584246 cites W2079088811 @default.
- W2106584246 cites W2116334708 @default.
- W2106584246 hasPublicationYear "1972" @default.
- W2106584246 type Work @default.
- W2106584246 sameAs 2106584246 @default.
- W2106584246 citedByCount "0" @default.
- W2106584246 crossrefType "journal-article" @default.
- W2106584246 hasAuthorship W2106584246A5010835041 @default.
- W2106584246 hasConcept C10390562 @default.
- W2106584246 hasConcept C105795698 @default.
- W2106584246 hasConcept C12426560 @default.
- W2106584246 hasConcept C127413603 @default.
- W2106584246 hasConcept C134306372 @default.
- W2106584246 hasConcept C202444582 @default.
- W2106584246 hasConcept C205203396 @default.
- W2106584246 hasConcept C2524010 @default.
- W2106584246 hasConcept C28826006 @default.
- W2106584246 hasConcept C31447003 @default.
- W2106584246 hasConcept C33923547 @default.
- W2106584246 hasConcept C5917680 @default.
- W2106584246 hasConcept C66938386 @default.
- W2106584246 hasConcept C78383375 @default.
- W2106584246 hasConceptScore W2106584246C10390562 @default.
- W2106584246 hasConceptScore W2106584246C105795698 @default.
- W2106584246 hasConceptScore W2106584246C12426560 @default.
- W2106584246 hasConceptScore W2106584246C127413603 @default.
- W2106584246 hasConceptScore W2106584246C134306372 @default.
- W2106584246 hasConceptScore W2106584246C202444582 @default.
- W2106584246 hasConceptScore W2106584246C205203396 @default.
- W2106584246 hasConceptScore W2106584246C2524010 @default.
- W2106584246 hasConceptScore W2106584246C28826006 @default.
- W2106584246 hasConceptScore W2106584246C31447003 @default.
- W2106584246 hasConceptScore W2106584246C33923547 @default.
- W2106584246 hasConceptScore W2106584246C5917680 @default.
- W2106584246 hasConceptScore W2106584246C66938386 @default.
- W2106584246 hasConceptScore W2106584246C78383375 @default.
- W2106584246 hasLocation W21065842461 @default.
- W2106584246 hasOpenAccess W2106584246 @default.
- W2106584246 hasPrimaryLocation W21065842461 @default.
- W2106584246 hasRelatedWork W1410897694 @default.
- W2106584246 hasRelatedWork W1533055875 @default.
- W2106584246 hasRelatedWork W155955584 @default.
- W2106584246 hasRelatedWork W157077504 @default.
- W2106584246 hasRelatedWork W1964874733 @default.
- W2106584246 hasRelatedWork W1967927086 @default.
- W2106584246 hasRelatedWork W1972722841 @default.
- W2106584246 hasRelatedWork W202130741 @default.
- W2106584246 hasRelatedWork W2026389556 @default.
- W2106584246 hasRelatedWork W2031589874 @default.
- W2106584246 hasRelatedWork W2042906951 @default.
- W2106584246 hasRelatedWork W2094371284 @default.
- W2106584246 hasRelatedWork W2312204873 @default.
- W2106584246 hasRelatedWork W2482182568 @default.
- W2106584246 hasRelatedWork W2912279866 @default.
- W2106584246 hasRelatedWork W2915228020 @default.
- W2106584246 hasRelatedWork W2999267087 @default.
- W2106584246 hasRelatedWork W3018499750 @default.
- W2106584246 hasRelatedWork W3024044053 @default.
- W2106584246 hasRelatedWork W3212068440 @default.
- W2106584246 isParatext "false" @default.
- W2106584246 isRetracted "false" @default.
- W2106584246 magId "2106584246" @default.
- W2106584246 workType "article" @default.