# On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines

## Abstract

The purpose of this paper is to construct new types of wavelets for minimal splines on an irregular grid. The approach applied to construct spline-wavelet decompositions uses approximation relations as an initial structure for constructing the spaces of minimal splines. The advantages of this approach are the possibilities of using irregular grids and sufficiently arbitrary nonpolynomial spline-wavelets.

- Authors:

- St.Petersburg State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773917

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; DECOMPOSITION; MATHEMATICAL SPACE; SPLINE FUNCTIONS

### Citation Formats

```
Makarov, A. A., E-mail: a.a.makarov@spbu.ru.
```*On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3920-Z.

```
Makarov, A. A., E-mail: a.a.makarov@spbu.ru.
```*On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines*. United States. doi:10.1007/S10958-018-3920-Z.

```
Makarov, A. A., E-mail: a.a.makarov@spbu.ru. Wed .
"On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines". United States. doi:10.1007/S10958-018-3920-Z.
```

```
@article{osti_22773917,
```

title = {On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines},

author = {Makarov, A. A., E-mail: a.a.makarov@spbu.ru},

abstractNote = {The purpose of this paper is to construct new types of wavelets for minimal splines on an irregular grid. The approach applied to construct spline-wavelet decompositions uses approximation relations as an initial structure for constructing the spaces of minimal splines. The advantages of this approach are the possibilities of using irregular grids and sufficiently arbitrary nonpolynomial spline-wavelets.},

doi = {10.1007/S10958-018-3920-Z},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 232,

place = {United States},

year = {2018},

month = {8}

}

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