A NUMERICAL STUDY ON HAMMERSLEY SEQUENCE AND FIBONACCI BASED LATTICE RULE FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS: A NUMERICAL STUDY ON HAMMERSLEY SEQUENCE AND FIBONACCI BASED LATTICE RULE FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS

Venelin  Todorov; Ivan  Dimov; Valerij  Dzurov; Tosho  Stanchev; Ilian  Tsvetkov; Valentin Dimitrov

doi:10.46687/jsar.v12i1.223

Authors

Venelin Todorov Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG
Ivan Dimov DEPARTMENT OF PARALLEL ALGORITHMS, IICT, BULGARIAN ACADEMY OF SCIENCES
Valerij Dzurov ROUSSE UNIVERSITY "ANGEL KANCHEV"
Tosho Stanchev ROUSSE UNIVERSITY ”ANGEL KANCHEV”
Ilian Tsvetkov ROUSSE UNIVERSITY ”ANGEL KANCHEV”
Valentin Dimitrov ROUSSE UNIVERSITY "ANGEL KANCHEV"

DOI:

https://doi.org/10.46687/jsar.v12i1.223

Keywords:

Quasi-Monte Carlo sequences, multidimensional integrals, Hammersley sequence, Fibonacci lattice rule, Sobol sequence, applications

Abstract

In this paper we make a numerical study between Hammersley quasi-random sequence and Fibonacci based lattice rule for computing multidimensional integrals. The two methods have not been compared before and both are recommended in case of smooth integrands. The two quasi-Monte Carlo approaches are completely different thus it is a question of interest which one of them outperforms the other. We consider a case study with smooth integrand functions of different dimensions. A comparison with Sobol sequence for a fixed computational time is given.

Author Biographies

Venelin Todorov, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG

Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG

https://orcid.org/0000-0001-7134-5901

Ivan Dimov, DEPARTMENT OF PARALLEL ALGORITHMS, IICT, BULGARIAN ACADEMY OF SCIENCES

DEPARTMENT OF PARALLEL ALGORITHMS, IICT, BULGARIAN ACADEMY OF SCIENCES

Valerij Dzurov, ROUSSE UNIVERSITY "ANGEL KANCHEV"

ROUSSE UNIVERSITY "ANGEL KANCHEV"

Tosho Stanchev, ROUSSE UNIVERSITY ”ANGEL KANCHEV”

ROUSSE UNIVERSITY ”ANGEL KANCHEV”

Ilian Tsvetkov, ROUSSE UNIVERSITY ”ANGEL KANCHEV”

ROUSSE UNIVERSITY ”ANGEL KANCHEV”

Valentin Dimitrov, ROUSSE UNIVERSITY "ANGEL KANCHEV"

ROUSSE UNIVERSITY "ANGEL KANCHEV"

A NUMERICAL STUDY ON HAMMERSLEY SEQUENCE AND FIBONACCI BASED LATTICE RULE FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS