Dynamics with Matrices Possessing Kronecker Product Structure
نویسندگان
چکیده
منابع مشابه
Approximation of functions of large matrices with Kronecker structure
We consider the numerical approximation of f(A)b where b ∈ R and A is the sum of Kronecker products, that is A = M2 ⊗ I + I ⊗ M1 ∈ RN×N . Here f is a regular function such that f(A) is well defined. We derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations, with special emphasis on the exponential function, for ...
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We propose a constructive algorithm, called the tensor-based Kronecker product (KP) singular value decomposition (TKPSVD), that decomposes an arbitrary real matrix A into a finite sum of KP terms with an arbitrary number of d factors, namely A = ∑R j=1 σj A dj ⊗ · · · ⊗A1j . The algorithm relies on reshaping and permuting the original matrix into a d-way tensor, after which its tensor-train ran...
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The generalized defect D(U) of a unitary N ×N matrix U with no zero entries is the dimension of the real space of directions, moving into which from U we do not disturb the moduli |Ui,j | as well as the Gram matrix U∗U in the first order. Then the defect d(U) is equal to D(U) − (2N − 1), that is the generalized defect diminished by the dimension of the manifold {DrUDc : Dr,Dc unitary diagonal}....
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ژورنال
عنوان ژورنال: Procedia Computer Science
سال: 2015
ISSN: 1877-0509
DOI: 10.1016/j.procs.2015.05.243