نتایج جستجو برای: rank k update
تعداد نتایج: 512739 فیلتر نتایج به سال:
Let A ∈ Mn(C ). We give a rank characterization of the semidefiniteness of Hermitian A in two ways. We show that A is semidefinite if and only if rank[X∗AX] = rank[AX], for all X ∈ Mn(C ), and we show that A is semidefinite if and only if rank[X∗AX] = rank[AXX∗], for all X ∈ Mn(C ). We show that if A has semidefinite Hermitian part and A has positive semidefinite Hermitian part then A satisfies...
In this paper we present a general formalism for the establishment of the family of selective partial update affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU partial rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms...
Let K be a field and let V be a vector space of finite dimension n over K. We investigate properties of a subspaceM of EndK(V ) of dimension n(n − r + 1) in which each non-zero element of M has rank at least r and show that such subspaces exist if K has a cyclic Galois extension of degree n. We also investigate the maximum dimension of a constant rank r subspace of EndK(V ) when K is finite.
We study low-rank approximation in the streaming model in which the rows of an n × d matrix A are presented one at a time in an arbitrary order. At the end of the stream, the streaming algorithm should output a k × d matrix R so that ‖A−ARR‖F ≤ (1 + )‖A−Ak‖F , where Ak is the best rank-k approximation to A. A deterministic streaming algorithm of Liberty (KDD, 2013), with an improved analysis of...
Abstract. Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C-algebra, C(Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C(Λ). The Kgroups of C(Λ) for k > 2 can be calculated under certain circumstances and we consider the case k = 3. We prove that for arbitrary k, the torsion-free rank of K0(C∗(Λ)) and K1(C∗(Λ)) ...
Let M k be the moduli space of based (anti-self-dual) instantons on CP 2 of charge k and rank n. There is a natural inclusion M k →֒ M n+1 k . We show that the direct limit space M∞ k is homotopy equivalent to BU(k)× BU(k). Let l∞ be a line in the complex projective plane and let C̃P 2 be the blow-up at a point away from l∞. Mnk can be alternatively described as the moduli space of rank n holomor...
In convex nonnegative matrix factorization, the feature vectors are modeled by convex combinations of observation vectors. In the paper, we propose to express the factorization model in terms of the sum of rank-1 matrices. Then the sparse factors can be easily estimated by applying the concept of the Hierarchical Alternating Least Squares (HALS) algorithm which is still regarded as one of the m...
In this paper, we present a generalized Symmetric Rank-one (SR1) method by employing interpolatory polynomials in order to possess a more accurate information from more than one previous step. The basic idea is to incorporate the SR1 update within the framework of multi-step methods. Hence iterates could be interpolated by a curve in such a way that the consecutive points define the curves. How...
Preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite (SPD) Jacobian. Following the theoretical work in [1] we start from a given approximation of the inverse of the initial Jacobian, and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems arising in the Picard-Newton solution of...
We show that a time series x(t) evolving by a nonlocal update rule x(t) =f (x(t-n),x(t-k)) with two different delays k < n can be mapped onto a local process in two dimensions with special time-delayed boundary conditions, provided that n and k are coprime. For certain stochastic update rules exhibiting a nonequilibrium phase transition, this mapping implies that the critical behavior does not ...
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