Adaptive order polynomial algorithm in a multiwavelet representation scheme

被引：8

作者：

Durdek, Antoine ^{[1
]}

Jensen, Stig Rune ^{[2
]}

Juselius, Jonas ^{[3
]}

Wind, Peter ^{[3
]}

Fla, Tor ^{[1
]}

Frediani, Luca ^{[3
]}

机构：

[1] Univ Tromso, Dept Math, Ctr Theoret & Computat Chem, N-9037 Tromso, Norway

[2] Univ Tromso, Dept Phys, Ctr Theoret & Computat Chem, N-9037 Tromso, Norway

[3] Univ Tromso, Dept Chem, Ctr Theoret & Computat Chem, N-9037 Tromso, Norway

来源：

APPLIED NUMERICAL MATHEMATICS | 2015年 / 92卷

关键词：

Wavelets; Legendre polynomials; Representation; Optimization; Multiwavelets; Adaptivity; Compression; MULTIRESOLUTION QUANTUM-CHEMISTRY; PARTIAL-DIFFERENTIAL-EQUATIONS; DENSITY-FUNCTIONAL THEORY; MOLECULAR-DYNAMICS; BASES; ENERGY;

D O I：

10.1016/j.apnum.2014.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We have developed a new strategy to reduce the storage requirements of a multivariate function in a multiwavelet framework. We propose that alongside the commonly used adaptivity in the grid refinement one can also vary the order of the representation k as a function of the scale n. In particular the order is decreased with increasing refinement scale. The consequences of this choice, in particular with respect to the nesting of scaling spaces, are discussed and the error of the approximation introduced is analyzed. The application of this method to some examples of mono- and multivariate functions shows that our algorithm is able to yield a storage reduction up to almost 60%. In general, values between 30 and 40% can be expected for multivariate functions. Monovariate functions are less affected but are also much less critical in view of the so called "curse of dimensionality". (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：40 / 53

页数：14

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