Matches in SemOpenAlex for { <https://semopenalex.org/work/W2014604383> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W2014604383 endingPage "193" @default.
- W2014604383 startingPage "176" @default.
- W2014604383 abstract "This paper is concerned with the estimation of the L 1 norm of the difference between a function f of bounded variation in [0, 1] and the associated variation-diminishing spline function with equidistant knots, S m,n f, with see Schoenberg [4]. For f bounded on [0, 1] and for integers m, n such that $$ n geqslant m geqslant 2, $$(1.1)the function S m,n f is defined by $$ S_{m.n} fleft( x right) = sumlimits_{j = 0}^iota {fleft( {n^{ - 1} xi left( {m,j} right)} right)bar N_{m.j} left( {nx} right),} $$(1.2)where $$ l = m + n - 2, $$(1.3)$$xi left( {m,j} right) = left{ {begin{array}{*{20}{c}} {frac{{left( {j + 1} right)j}}{{2left( {m - 1} right)}},} hfill & {j = 0, ldots ,m - 2} hfill {j + 1 - frac{m}{2},} hfill & {j = m - 1, ldots ,n - 1,} hfill {n - xi left( {m,l - j} right),} hfill & {j = n, ldots ,l,} hfill end{array} } right.$$(1.4)$${{tilde{N}}_{{m,jleft( x right)}}} = left{ {begin{array}{*{20}{c}} {frac{{j + 1}}{m}{{h}_{{m.j + 1}}}left( x right),} hfill & {j = 0, ldots ,m - 2,} hfill {{{h}_{m}}left( {x + m - j - 1} right),} hfill & {j = m - 1, ldots ,n - 1,} hfill {{{{bar{N}}}_{{m.l - j}}}left( {n - x} right),} hfill & {j = n, ldots ,l,} hfill end{array} } right.$$(1.5)$${{h}_{{m,k}}}left( x right) = frac{m}{{k!}}sumlimits_{{i = 1}}^{k} {{{{( - 1)}}^{{k - i}}}{{i}^{{k - m}}}} left( {_{i}^{k}} right)left( {i - x} right)_{ + }^{{m - 1}}{mkern 1mu} {text{for }}x0,$$(1.6)$$ h_m left( x right) = h_{m.m} left( x right).$$(1.7)." @default.
- W2014604383 created "2016-06-24" @default.
- W2014604383 creator A5036383066 @default.
- W2014604383 date "1974-06-01" @default.
- W2014604383 modified "2023-10-16" @default.
- W2014604383 title "The L1 norm of the approximation error for splines with equidistant knots" @default.
- W2014604383 cites W1512171754 @default.
- W2014604383 cites W2022681869 @default.
- W2014604383 cites W4234562099 @default.
- W2014604383 cites W4253560234 @default.
- W2014604383 doi "https://doi.org/10.1016/0021-9045(74)90030-6" @default.
- W2014604383 hasPublicationYear "1974" @default.
- W2014604383 type Work @default.
- W2014604383 sameAs 2014604383 @default.
- W2014604383 citedByCount "6" @default.
- W2014604383 countsByYear W20146043832013 @default.
- W2014604383 countsByYear W20146043832014 @default.
- W2014604383 crossrefType "journal-article" @default.
- W2014604383 hasAuthorship W2014604383A5036383066 @default.
- W2014604383 hasBestOaLocation W20146043831 @default.
- W2014604383 hasConcept C122383733 @default.
- W2014604383 hasConcept C127413603 @default.
- W2014604383 hasConcept C134306372 @default.
- W2014604383 hasConcept C158245278 @default.
- W2014604383 hasConcept C17744445 @default.
- W2014604383 hasConcept C191795146 @default.
- W2014604383 hasConcept C199539241 @default.
- W2014604383 hasConcept C2524010 @default.
- W2014604383 hasConcept C2779863119 @default.
- W2014604383 hasConcept C28826006 @default.
- W2014604383 hasConcept C33923547 @default.
- W2014604383 hasConcept C42360764 @default.
- W2014604383 hasConceptScore W2014604383C122383733 @default.
- W2014604383 hasConceptScore W2014604383C127413603 @default.
- W2014604383 hasConceptScore W2014604383C134306372 @default.
- W2014604383 hasConceptScore W2014604383C158245278 @default.
- W2014604383 hasConceptScore W2014604383C17744445 @default.
- W2014604383 hasConceptScore W2014604383C191795146 @default.
- W2014604383 hasConceptScore W2014604383C199539241 @default.
- W2014604383 hasConceptScore W2014604383C2524010 @default.
- W2014604383 hasConceptScore W2014604383C2779863119 @default.
- W2014604383 hasConceptScore W2014604383C28826006 @default.
- W2014604383 hasConceptScore W2014604383C33923547 @default.
- W2014604383 hasConceptScore W2014604383C42360764 @default.
- W2014604383 hasIssue "2" @default.
- W2014604383 hasLocation W20146043831 @default.
- W2014604383 hasOpenAccess W2014604383 @default.
- W2014604383 hasPrimaryLocation W20146043831 @default.
- W2014604383 hasRelatedWork W1593400972 @default.
- W2014604383 hasRelatedWork W1984783084 @default.
- W2014604383 hasRelatedWork W2017419110 @default.
- W2014604383 hasRelatedWork W2035156587 @default.
- W2014604383 hasRelatedWork W2071616196 @default.
- W2014604383 hasRelatedWork W2138659731 @default.
- W2014604383 hasRelatedWork W2161741483 @default.
- W2014604383 hasRelatedWork W2990473846 @default.
- W2014604383 hasRelatedWork W4241254601 @default.
- W2014604383 hasRelatedWork W4245585316 @default.
- W2014604383 hasVolume "11" @default.
- W2014604383 isParatext "false" @default.
- W2014604383 isRetracted "false" @default.
- W2014604383 magId "2014604383" @default.
- W2014604383 workType "article" @default.