On spectral data and tensor decompositions in Finslerian framework

[1] K. C. Chang, K. Pearson and T. Zhang, On eigenvalue problems of real symmetric tensors, Journal of Mathematical Analysis and Applications 350 (2009), 416-422.

[2] L. Qi, Eigenvalues of a real supersymmetric tensor, Jour. Symb. Comp. 40 (2005), 1302-1324.

[3] A. Cichocki, N. Lee, I. V. Oseledets, A. H. Phan, Q. Zhao and D. P. Mandic, Tensor networks for dimensionality reduction and large-scale optimization: part 1 low-rank tensor decompositions, Found. Trends Mach. Learn. 9 (4-5) (2016), 249-429.

[4] P. Comon, Tensor diagonalization, a useful tool in signal processing, In: IFAC-SYSID, 10th IFAC Symposium on System Identification (Copenhagen, Denmark, July 4-6, 1994. Invited Session), Blanke M., Soderstrom T. (eds), 1 (1994), 77-82.

[5] B. Jiang, S. Ma and S. Zhang, Tensor principal component analysis via convex optimization, Mathematical Programming 150, 2 (2015), 423-457.

[6] L. de Lathauwer, B. de Moor and J. Vandewalle, A multilinear SVD, SIAM J. Matrix Anal. Appl. 21 (2000), 1253-1278.

[7] L. Qi, W. Sun and Y. Wang, Numerical multilinear algebra and its applications, Front. Math. China 2(4) (2007), 501-526.

[8] N. Vannieuwenhoven, N. Vanbaelen, K. Meerbergen and R. Vandebril, The dense multiple-vector tensor-vector product: An initial study, Report TW 635, Katholieke Universiteit Leuven, Department of Computer Science, 2013.

[9] Z. Shen, Differential geometry of spray and Finsler spaces, Springer, 2001.

[10] D. Bao, S-S. Chern and Z. Shen, An introduction to Riemann-Finsler geometry, Springer-Verlag, 2000.

[11] I. Bucataru and R. Miron, Finsler-Lagrange geometry. Applications to dynamical systems, Editura Academiei Romane, Bucuresti, 2007.

[12] X. Cheng and Z. Shen, Finsler Geometry: An Approach via Randers Spaces, Springer, 2013.

[13] R. Miron and M. Anastasiei, Vector bundles. Lagrange spaces. Applications to relativity, Geometry Balkan Press, 1996.

[14] V. Balan, Spectra of multilinear forms associated to notable m-root relativistic models, Linear Algebra and Appl. (LAA), online http://dx.doi.org/10.1016/j.laa.2011.06.033; 436, 1, 1 (2012), 152-162. [15] V. Balan, Spectral properties and applications of numerical multilinear algebra of m−th root structures, Hypercomplex Numbers in Geom. Phys. 2(10), 5 (2008), 101-107.

[16] V. Balan, G. Bogoslovsky, S. Kokarev, D. Pavlov, S. Syparov and N. Voicu, Geometrical models of the locally anisotropic Space-Time, Hypercomplex Numbers in Geom. Phys., Moscow, 1(15), 8 (2011), 4-37.

[17] M. D. Cirillo, R. Mirdell, F. Sjoberg and T. Pham, Tensor decomposition for colour image segmentation of burn wounds, Sci. Rep. 9 (2019), 3291.

[18] Y. Zhang, J. Liu, S. Yang and Z. Guo, Joint image denoising using self-similarity based low-rank approxima[1]tions, Institute of Computer Science and Technology, Peking University, Beijing 100871, China; 2013 Visual Communications and Image Processing (VCIP).

[19] D. Goldfarb and Z. (Tony) Qin, Robust Low-Rank Tensor Recovery: Models and Algorithms, SIAM J. Matrix Anal. Appl., 35(1) (2019), 225-253.

[20] S. Zhang, X. Guo, X. Xu, L. Li andC-C Chang, A video watermark algorithm based on tensor decomposition, Math Biosci Eng. 16(5) (2019), 3435-3449.

[21] J. Li, J. Bien and M. Wells, HO-SVD package, 2019; https://rdrr.io/github/jamesyili/rTensor/

[22] , MATLAB Tensor Toolbox, Version 2.6.

[23] , Tensorlab demos, www.tensorlab.net/demos/basic.html, www.tensorlab.net/demos/mlsvd.html.

[24] , Sandia Laboratories webpage, https://www.sandia.gov/ tgkolda/TensorToolbox/reg-2.6.html

[25] , Tensor Toolbox webpage, https://www.tensortoolbox.org

[26] , Htucker webpage (Matlab toolbox for HO-SVD), Czech Republic, https://www.swmath.org/software/9637

[27] V. Balan and N. Perminov, Applications of resultants in the spectral m-root framework, Appl. Sci. (APPS), 12 (2010), 20-29.

[28] V. Balan, H. V. Grushevskaya, N. G. Krylova, M. Neagu and A. Oana, On the Berwald-Lagrange scalar curvature in the structuring process of the LB-monolayer, Applied Sciences 15 (2013), 30-42.

[29] V. Balan, H. V. Grushevskaya and N. G. Krylova, Finsler geometry approach to thermodynamics of first order phase transitions in monolayers, Differential Geometry - Dynamical Systems, 17 (2015), 24-31.

[30] V. Balan and J. Stojanov, Finsler-type estimators for the cancer cell population dynamics, Publications de l’Institut Mathematique, Publisher: Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd, 98(112) (2015), 53-69.

[31] V. Balan, J. Stojanov, Anisotropic metric models in the Garner oncologic framework, ROMAI J. 10, 1 (2014), 1-10.

[32] L. Astola and L. Florack, Finsler Geometry on higher order tensor fields and applications to High Angular Res[1]olution Diffusion Imaging, International Journal of Computer Vision 5567 (3) (2009), 224-234, DOI:10.1007/978- 3-642-02256-2 19.

[33] H. Shimada, On Finsler spaces with the metric L = pn ai1i2...in (x)y i1 y i2 . . . yin , Tensor N.S., 33 (1979), 365-372.

[34] P. L. Antonelli, R. S. Ingarden and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, Kluwer Academic Publishers, Fundamental Theories of Physics 58, Netherlands, 1993.