New Kronecker product decompositions and its applications
نویسنده
چکیده
Firstly, two new kinds of Kronecker decompositions is developed, i.e. KPGD and KPID; Secondly, the sufficient and necessary conditions and algorithms of Kronecker product(KPD), KPGD, and KPID are discussed; At last, some useful properties of the rank of the sum of Kronecker product gemel decompositions are obtained.
منابع مشابه
Kronecker Product Approximation for Three-Dimensional Imaging Applications
Kronecker product and tensor decompositions are used to construct approximations of severely ill-conditioned matrices that arise in three-dimensional image processing applications. Computa-tionally efficient methods to construct the approximations are developed by exploiting structure that is inherent in many image processing problems, such as those arising in microscopy and medical imaging. It...
متن کاملThe Kronecker Product and Stochastic Automata Networks
This paper can be thought of as a companion paper to Van Loan’s The Ubiquitous Kronecker Product paper [23]. We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a Stochastic Automata Network preconditioner. We conclude by describing one application of the Kronecker product,...
متن کاملShifted Kronecker Product Systems
Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...
متن کاملSymmetric Kronecker Products and Semiclassical Wave Packets
We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.
متن کاملOn Edge Exchanges in Hamiltonian Decompositions of Kronecker-product Graphs
Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (...
متن کامل