ac0e095a-ee09-4fe1-9c46-887bf9f8fc6120210319062715760wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195Spaces of the Haar Type on Arbitrary Irregular GridsYu. K.Dem’yanovichDept. of Parallel Computations, Dept. of Computational Mathematics, St. Petersburg State University, St. Petersburg, RUSSIAI. G.BurovaDept. of Parallel Computations, Dept. of Computational Mathematics, St. Petersburg State University, St. Petersburg, RUSSIAThe paper deals with Haar-type spaces on arbitrary irregular grids. The choice of non-uniform grids determines the characteristics of the Haar-type space that can be used to construct the wavelet decomposition. Thus, it becomes a possible adaptive choice of the design space depending on the incoming flow. In contrast to the classical approach, this paper considers the possibility of the adaptive compression of the initial flow. The complexity of the algorithm is directly proportional to the length of the initial number flow. Numerical examples are presented.11520201152020592600https://www.wseas.org/multimedia/journals/control/2020/b185103-029.pdf10.37394/23203.2020.15.59https://www.wseas.org/multimedia/journals/control/2020/b185103-029.pdf10.1007/s00574-017-0055-7I. Singh, S. Kumar, Haar Wavelet Methods for Numerical Solutions of Harry Dym (HD), BBM Burger’s and 2D Diffusion Equations, Bulletin of the Brazilian Mathematical Society,Vol.49, No 2, 2018, pp. 313-338. DOI: 10.1007/s00574-017-0055-7. 10.1016/j.physa.2019.123738N. Pervaiz, I. Aziz, Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations, Physica A: Statistical Mechanics and its Applications, Vol. 545, paper 123738, 2020, DOI: 10.1016/j.physa.2019.123738. 10.1007/978-981-13-9608-3_14A Raza, A. Khan, Approximate solution of higher order two point boundary value problems using uniform Haar wavelet collocation method, Springer Proceedings in Mathematics and Statistics, 272, 2019, pp. 209-220. DOI: 10.1007/978-981-13-9608-3_14. 10.3390/s20071962R. Amin, S. Nazir, I. García-Magariño, A collocation method for numerical solution of nonlinear delay integro-differential equations for wireless sensor network and internet of things Sensors (Switzerland),Vol 20,7, paper 1962, 2020. 10.1007/s00034-019-01285-wE.H.S. Diop, A.-O. Boudraa, V.B.S Prasath, Optimal Nonlinear Signal Approximations Based on Piecewise Constant Functions, Circuits, Systems, and Signal Processing, Vol. 39, No 5, 2020, pp. 2673-2694. DOI: 10.1007/s00034-019-01285.10.1007/bf01456326A.Haar Zur, Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, 69, 1910, pp. 331–371.https://link.springer.com/article/10.1007/BF01456326S.Mallat A WaveletTour of Signal Processing,Academic Press, 1999. DOI: 10.2118/96553-MS. 10.1016/j.amc.2003.09.021Francois Dubeau, Said Elmejdani, Riadh Ksantini, Non-uniform Haar wavelets, Applied Mathematics and Computation, Vol.159, 2004, pp. 675–691,https://www.sciencedirect.com/science/article /abs/pii/S009630030301155X 10.1007/s10958-015-2571-6Yu. K.Demyanovich, A.Yu.Ponomareva, Adaptive Spline-Wavelet Processing of a Discrete Flow, J. Math. Sci., New York,Vol.210, No 4, 2015, pp.371–390. DOI: 10.1007/s10958-015-2571-6. 10.1049/iet-gtd.2019.0662H, Saxena, A. Singh, J.N. Rai, Adaptive spline-based PLL for synchronisation and power quality improvement in distribution system, IET Generation, Transmission and Distribution, Vol. 14, No 7, 2020, pp. 1311–1319. 10.1111/cgf.13669D.Cornel, A.Buttinger-Kreuzhuber, A.Konev, Z.Horvath, M.Wimmer, R. Heidrich, J.Waser, Interactive visualization of flood and heavy rain simulations, Computer Graphics Forum, Vol.38, No 3, 2019, pp. 25–29.10.1016/j.ijepes.2019.105577Z.Yang, H.Liu, T.Bi, Z.Li, Q.Yang, An adaptive PMU missing data recovery method, International Journal of Electrical Power and Energy Systems,Vol.116, paper 105577, 2020. I.G.Burova, E.F.Muzafarova, D.E.Zhilin, About adaptive grids construction, WSEAS Transactions on Mathematics, Vol.17, 2018, pp. 340–351. I.G.Burova,I.I.Narbutovskikh, E.F.Muzafarova,Image Processing and the Spline Approximation of the Third and Fifth Order, International Journal of Circuits, Systems and Signal Processing, Vol. 13, 2019, pp. 550- 557.10.37394/23206.2020.19.7I.G.Burova,E.F.Muzafarova,I.I.Narbutovskikh, Local splines of the Second and Third Order, Complex-valued Splines and Image Processing, pp. 419-429, International Journal of Circuits, Systems and Signal Processing, Vol. 13, 2019.Yu. K. Dem’yanovich, General Flows and their Adaptive Decompositions, WSEAS Transactions on Mathematics, Volume 17, 2018, pp. 28-34. Maple 2017.0, Product Build IDs, Maple Build ID 1231047, Licensed to: Prof. Yuri Demyanovich, Serial Number: M4SUJR24AKMC7YDY, Permanent Licence.10.1016/s1095-6433(01)00384-1Vladimir Zhuravlev, Vladislav Bugaj, Sodikdjon Kodirov, Tatiana Safonova, Alexandr Staruschenko, Giant multimodal heart motoneurons of Achatina fulica: a new cardioregulatory input in pulmonates, Comparative Biochemistry and Physiology Part A, Vol. 130, 2001, pp.183-196.