On subspace distances determined by the Frobenius norm
نویسندگان
چکیده
منابع مشابه
Title Subspace segmentation with a minimal square frobenius norm
We introduce a novel subspace segmentation method called Minimal Squared Frobenius Norm Representation (MSFNR). MSFNR performs data clustering by solving a convex optimization problem. We theoretically prove that in the noiseless case, MSFNR is equivalent to the classical Factorization approach and always classifies data correctly. In the noisy case, we show that on both synthetic and real-word...
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Let p′ and q′ be points in R. Write p′ ∼ q′ if p′ − q′ is a multiple of (1, . . . , 1). Two different points p and q in R/ ∼ uniquely determine a tropical line L(p, q) passing through them and stable under small perturbations. This line is a balanced unrooted semi–labeled tree on n leaves. It is also a metric graph. If some representatives p′ and q′ of p and q are the first and second columns o...
متن کاملComments on “ Is the Frobenius Matrix Norm Induced ? ”
In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...
متن کاملAuthors' reply - Comments on "Is the frobenius matrix norm induced?"
In a paper [1] the authors ask whether the Frobenius and the H norms are induced. There they claimed that the Frobenius norm is not induced, and consequently conjectured that the H-norm may not be induced. In this note it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H-norm is in fact induced on a particular matrix-valued L1 space. NOTATION R...
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In this paper we introduce a new method for defining preconditioners for the iterative solution of a system of linear equations. By generalizing the class of modified preconditioners (e.g. MILU), the interface probing, and the class of preconditioners related to the Frobenius norm minimization (e.g. FSAI, SPAI) we develop a toolbox for computing preconditioners that are improved relative to a g...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.01.017