QUADRATIC SPLINE WAVELETS WITH SHORT SUPPORT SATISFYING HOMOGENEOUS BOUNDARY CONDITIONS

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dc.contributor.authorČerná, Dana
dc.contributor.authorFiněk, Václav
dc.date.accessioned2019-08-30T06:59:33Z
dc.date.available2019-08-30T06:59:33Z
dc.date.issued2018-01-01
dc.description.abstractIn this paper, we construct a new quadratic spline-wavelet basis on the interval and on the unit square satisfying homogeneous Dirichlet boundary conditions of the first order. The wavelets have one vanishing moment and the shortest support among quadratic spline wavelets with at least one vanishing moment adapted to the same type of boundary conditions. The stiffness matrices arising from the discretization of the second-order elliptic problems using the constructed wavelet basis have uniformly bounded condition numbers, and the condition numbers are small. We present some quantitative properties of the constructed basis. We provide numerical examples to show that the Galerkin method and the adaptive wavelet method using our wavelet basis require fewer iterations than methods with other quadratic spline wavelet bases. Moreover, due to the small support of the wavelets, when using these methods with the new wavelet basis, the system matrix is sparser, and thus one iteration requires a smaller number of floating point operations than for other quadratic spline wavelet bases.cs
dc.format.extent25 strancs
dc.identifier.doi10.1553/etna_vol48s15
dc.identifier.urihttps://dspace.tul.cz/handle/15240/153346
dc.identifier.urihttps://epub.oeaw.ac.at/0xc1aa5576_0x00376305.pdf
dc.language.isocscs
dc.relation.ispartofELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
dc.subjectwaveletcs
dc.subjectquadratic splinecs
dc.subjecthomogeneous Dirichlet boundary conditionscs
dc.subjectcondition numbercs
dc.subjectelliptic problemcs
dc.titleQUADRATIC SPLINE WAVELETS WITH SHORT SUPPORT SATISFYING HOMOGENEOUS BOUNDARY CONDITIONScs
local.citation.epage39
local.citation.spage15
local.relation.volume48
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