论文信息 - Singular Value Decomposition of Complexes

Singular Value Decomposition of Complexes

Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two methods to compute them and present several applications.

[1] D. Eisenbud,et al. Equations and Syzygies of K3 Carpets and Unions of Scrolls , 2018, Acta Mathematica Vietnamica.

[2] R. Penrose. A Generalized inverse for matrices , 1955 .

[3] C. Eckart,et al. The approximation of one matrix by another of lower rank , 1936 .

[4] C. Voisin. green's canonical syzygy conjecture for generic curves of odd genus , 2003, Compositio Mathematica.

[5] K. Ranestad,et al. Varieties of sums of powers , 1998, math/9801110.

[6] D. Arnold,et al. Finite element exterior calculus, homological techniques, and applications , 2006, Acta Numerica.

[7] D. Arnold,et al. Finite element exterior calculus: From hodge theory to numerical stability , 2009, 0906.4325.

[8] Andreas Steenpaß,et al. Refined algorithms to compute syzygies , 2015, J. Symb. Comput..