On approximation of density function by shape preserving smoothing histospline

Svetlana Asmuss; Juris Breidaks; Natalja Budkina

On approximation of density function by shape preserving smoothing histospline

Svetlana Asmuss, Juris Breidaks, Natalja Budkina

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions, which are obtained from the properties of given histogram. The paper suggests the method for solving of the problem of histopolation when solution preserves some shape properties such as positivity, monotonicity and/or convexity. These conditions are considered as the positivity/negativity constraints on the derivative (or the derivatives) of approximants. The approach is illustrated by some numerical examples.

Original language	English
Title of host publication	APLIMAT 2016 - 15th Conference on Applied Mathematics 2016, Proceedings
Editors	Daniela Richtarikova, Dagmar Szarkova, L'udovit Balko
Place of Publication	Bratislava
Publisher	Slovak University of Technology in Bratislava
Pages	30-43
Number of pages	14
ISBN (Electronic)	978-802274531-4
Publication status	Published - 2016
Externally published	Yes
Event	15th Conference on Applied Mathematics (APLIMAT) - Bratislava, Slovakia Duration: 2 Feb 2016 → 4 Feb 2016 Conference number: 15 https://www.proceedings.com/29878.html http://toc.proceedings.com/29878webtoc.pdf

Conference

Conference	15th Conference on Applied Mathematics (APLIMAT)
Abbreviated title	APLIMAT 2016
Country/Territory	Slovakia
City	Bratislava
Period	2/02/16 → 4/02/16
Internet address	https://www.proceedings.com/29878.html http://toc.proceedings.com/29878webtoc.pdf

Keywords*

Density function
Histosplines
Shape preserving problem
Splines in convex sets

Field of Science*

1.1 Mathematics

Publication Type*

3.1. Articles or chapters in proceedings/scientific books indexed in Web of Science and/or Scopus database

Cite this

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title = "On approximation of density function by shape preserving smoothing histospline",

abstract = "The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions, which are obtained from the properties of given histogram. The paper suggests the method for solving of the problem of histopolation when solution preserves some shape properties such as positivity, monotonicity and/or convexity. These conditions are considered as the positivity/negativity constraints on the derivative (or the derivatives) of approximants. The approach is illustrated by some numerical examples.",

keywords = "Density function, Histosplines, Shape preserving problem, Splines in convex sets",

author = "Svetlana Asmuss and Juris Breidaks and Natalja Budkina",

year = "2016",

language = "English",

pages = "30--43",

editor = "Daniela Richtarikova and Dagmar Szarkova and L'udovit Balko",

booktitle = "APLIMAT 2016 - 15th Conference on Applied Mathematics 2016, Proceedings",

publisher = "Slovak University of Technology in Bratislava",

address = "Slovakia",

note = "15th Conference on Applied Mathematics (APLIMAT), APLIMAT 2016 ; Conference date: 02-02-2016 Through 04-02-2016",

url = "https://www.proceedings.com/29878.html, http://toc.proceedings.com/29878webtoc.pdf",

}

Asmuss, S, Breidaks, J & Budkina, N 2016, On approximation of density function by shape preserving smoothing histospline. in D Richtarikova, D Szarkova & L Balko (eds), APLIMAT 2016 - 15th Conference on Applied Mathematics 2016, Proceedings. Slovak University of Technology in Bratislava, Bratislava, pp. 30-43, 15th Conference on Applied Mathematics (APLIMAT), Bratislava, Slovakia, 2/02/16.

On approximation of density function by shape preserving smoothing histospline. / Asmuss, Svetlana; Breidaks, Juris; Budkina, Natalja.
APLIMAT 2016 - 15th Conference on Applied Mathematics 2016, Proceedings. ed. / Daniela Richtarikova; Dagmar Szarkova; L'udovit Balko. Bratislava: Slovak University of Technology in Bratislava, 2016. p. 30-43.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On approximation of density function by shape preserving smoothing histospline

AU - Asmuss, Svetlana

AU - Breidaks, Juris

AU - Budkina, Natalja

N1 - Conference code: 15

PY - 2016

Y1 - 2016

N2 - The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions, which are obtained from the properties of given histogram. The paper suggests the method for solving of the problem of histopolation when solution preserves some shape properties such as positivity, monotonicity and/or convexity. These conditions are considered as the positivity/negativity constraints on the derivative (or the derivatives) of approximants. The approach is illustrated by some numerical examples.

AB - The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions, which are obtained from the properties of given histogram. The paper suggests the method for solving of the problem of histopolation when solution preserves some shape properties such as positivity, monotonicity and/or convexity. These conditions are considered as the positivity/negativity constraints on the derivative (or the derivatives) of approximants. The approach is illustrated by some numerical examples.

KW - Density function

KW - Histosplines

KW - Shape preserving problem

KW - Splines in convex sets

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M3 - Conference contribution

AN - SCOPUS:84968610355

SP - 30

EP - 43

BT - APLIMAT 2016 - 15th Conference on Applied Mathematics 2016, Proceedings

A2 - Richtarikova, Daniela

A2 - Szarkova, Dagmar

A2 - Balko, L'udovit

PB - Slovak University of Technology in Bratislava

CY - Bratislava

T2 - 15th Conference on Applied Mathematics (APLIMAT)

Y2 - 2 February 2016 through 4 February 2016

ER -

On approximation of density function by shape preserving smoothing histospline

Abstract

Conference

Keywords*

Field of Science*

Publication Type*

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Cite this