Application of polynomial tensor interpolation for technical tests

• Autorzy: Ciekot Anita , Biernat Grzegorz , Frączek Tadeusz

Identyfikatory

DOI

10.17512/jamcm.2021.1.02

• Języki publikacji: EN

Abstrakty

EN

The main aim of this paper is a new formula of tensor interpolation by the polynomial of two variables. The formulas for interpolating polynomial coefficients are obtained using the Kronecker tensor product of matrices. The mathematical model for the diffusion process is presented. This paper is focused on determining the optimal parameters for this process by polynomial tensor interpolation of the obtained research results.

Słowa kluczowe

EN

polynomial tensor interpolation; Kronecker product; diffusion process

PL

wielomianowa interpolacja tensora; produkt Kroneckera; proces dyfuzji

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 1
• Strony: 17--24
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Ciekot Anita

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Biernat Grzegorz

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Frączek Tadeusz

• Faculty of Production Engineering and Materials Technology, Czestochowa University of Technology, Czestochowa, Poland

Bibliografia

• [1] Graham, A. (1981). Kronecker Products and Matrix Calculus with Applications. Ellis Horwood Ltd.
• [2] Kincaid, D., & Chnej, W. (2002). Numerical Analysis, Mathematics of Scientific Computing. The University of Texas at Austin.
• [3] Biernat, G., & Ciekot, A. (2009). The polynomial tensor interpolation. Arithmetical case. Scientific Research of the Institute of Mathematics and Computer Science Czestochowa University of Technology, 1(8), 7-11.
• [4] Frączek, T., Olejnik, M., Knapinski, M., & Biernat, G. (2010). Tensor interpolation of tribological wear in ionnitriding of 316L steel. Solid State Phenomena, 165, 43-49.
• [5] Olejnik, M. (2011). Niskotemperaturowe i krótkookresowe azotowanie jarzeniowe stali austenicznej X2CrNiMo 17012-2, PhD Thesis, Czestochowa (in Polish).
• [6] Biernat, G., & Ciekot, A. (2007). The polynomial interpolation for technical experiments. Scientific Research of the Institute of Mathematics and Computer Science Czestochowa University of Technology, 1(6), 19-22.
• [7] Gasca, M., & Sauer, T. (2000). On the history of multivariate polynomial interpolation. Journal of Computational and Applied Mathematics, 122, 23-35.
• [8] Thomas, D.H. (1976). A natural tensor product interpolation formula and pseudoinverse of a matrix. Linear Algebra and Its Applications, 13, 239-250.
• [9] Kilicman, A., & Al Zhour, Z.A.A. (2007). Kronecker operational matrices for fractional calculus and some applications. Applied Mathematics and Computation, 187, 250-265.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).