Optimized lattice rule and adaptive approach for multidimensional integrals with applications

• Autorzy: Todorov, Venelin , Dimov, Ivan , Fidanova, Stefka , Poryazov, Stoyan
• Konferencja: Federated Conference on Computer Science and Information Systems (16 ; 02-05.09.2021 ; online)
• Języki publikacji: EN

Abstrakty

EN

In this work we make a comparison between optimized lattice and adaptive stochastic approaches for multidimensional integrals with different dimensions. Some of the integrals has applications in environmental safety and control theory.

Słowa kluczowe

PL

optymalizacja; podejście stochastyczne; całka wielowymiarowa; wymiar; bezpieczeństwo środowiska; teoria sterowania

EN

optimization; stochastic approach; multidimensional integral; dimension; environmental safety; control theory

• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2021
• Tom: Vol. 26
• Strony: 75--80
• Opis fizyczny: Bibliogr. 12 poz., wz., tab.

Twórcy

autor

Todorov, Venelin

• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,
• Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 25A Acad. G. Bonchev Str., 1113 Sofia, Bulgaria

autor

Dimov, Ivan

• Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 25A Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,

autor

Fidanova, Stefka

• Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 25A Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,

autor

Poryazov, Stoyan

• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,

Bibliografia

• 1. Berntsen J., Espelid T.O., Genz A. (1991) An adaptive algorithm for the approximate calculation of multiple integrals, ACM Trans. Math. Softw. 17: 437–451.
• 2. Dimov I. (2008) Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, 291 p., ISBN-10 981-02-2329-3.
• 3. Dimov I., Karaivanova A., Georgieva R., Ivanovska S. (2003) Parallel Importance Separation and Adaptive Monte Carlo Algorithms for Multiple Integrals, Springer Lecture Notes in Computer Science, 2542, 99–107.
• 4. Dimov I., Georgieva R. (2010) Monte Carlo Algorithms for Evaluating Sobol’ Sensitivity Indices. Math. Comput. Simul. 81(3): 506–514.
• 5. A. Genz, Testing multidimensional integration routines. Tools, Methods and Languages for Scientific and Engineering Computation (1984) 81–94.
• 6. Hua L.K. and Wang Y. (1981) Applications of Number Theory to Numerical analysis.
• 7. Pencheva, V., I. Georgiev, and A. Asenov. “Evaluation of passenger waiting time in public transport by using the Monte Carlo method.” AIP Conference Proceedings. Vol. 2321. No. 1. AIP Publishing LLC, 2021.
• 8. Raeva, E., & Georgiev, I. R. (2018, October). Fourier approximation for modeling limit of insurance liability. In AIP Conference Proceedings (Vol. 2025, No. 1, p. 030006). AIP Publishing LLC.
• 9. I.F. Sharygin (1963) A lower estimate for the error of quadrature formulas for certain classes of functions, Zh. Vychisl. Mat. i Mat. Fiz. 3, 370–376.
• 10. I.H. Sloan and P.J. Kachoyan (1987) Lattice methods for multiple integration: Theory, error analysis and examples, SIAM J. Numer. Anal. 24, 116–128.
• 11. I.H. Sloan and S. Joe, Lattice Methods for Multiple Integration, Lattice methods for multiple Integration, (Oxford University Press 1994).
• 12. Y. Wang and F. J. Hickernell (2000) An historical overview of lattice point sets, in Monte Carlo and Quasi-Monte Carlo Methods 2000, Proceedings of a Conference held at Hong Kong Baptist University, China.

Uwagi

1. Preface

2. Session: 14th International Workshop on Computational Optimization

3. Communication Papers

Identyfikatory

DOI

10.15439/2021F94