A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format
暂无分享,去创建一个
[1] Peter Kosmol,et al. Methoden zur numerischen Behandlung nichtlinearer Gleichungen und Optimierungsaufgaben , 1989 .
[2] H. Schwetlick. Numerische Lösung nichtlinearer Gleichungen , 1978 .
[3] Wolfgang Hackbusch,et al. Canonical Tensor Products as a Generalization of Gaussian-type Orbitals , 2010 .
[4] Dietrich Braess,et al. F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Approximation of 1/x by Exponential Sums in [1, ∞) , 2022 .
[5] Gene H. Golub,et al. Rank-One Approximation to High Order Tensors , 2001, SIAM J. Matrix Anal. Appl..
[6] Martin J. Mohlenkamp,et al. Numerical operator calculus in higher dimensions , 2002, Proceedings of the National Academy of Sciences of the United States of America.
[7] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.
[8] S. D. Cutkosky,et al. Multilinear Algebra , 2019, Differential Forms.
[9] Martin J. Mohlenkamp,et al. Algorithms for Numerical Analysis in High Dimensions , 2005, SIAM J. Sci. Comput..
[10] T. Gasser,et al. Nonparametric Density Estimation under Unimodality and Monotonicity Constraints , 1999 .
[11] I. V. Oseledets,et al. Minimization methods for approximating tensors and their comparison , 2006 .
[12] Wolfgang Hackbusch,et al. Tensor product approximation with optimal rank in quantum chemistry. , 2007, The Journal of chemical physics.
[13] Boris N. Khoromskij,et al. Approximate iterations for structured matrices , 2008, Numerische Mathematik.
[14] W. Rheinboldt. Schwetlick H., Numerische Lösung nichtlinearer Gleichungen. Berlin VEB Deutscher Verlag der Wissenschaften 1979. 346 S., 21 Abb., M 68,— , 1980 .
[15] P. Paatero. A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .
[16] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[17] P. Paatero. The Multilinear Engine—A Table-Driven, Least Squares Program for Solving Multilinear Problems, Including the n-Way Parallel Factor Analysis Model , 1999 .