Matrix formulation for infinite-rank operators
نویسندگان
چکیده
منابع مشابه
On the Finite Rank of Bounded Semi-infinite Hankel Operators
Bounded, semi-infinite Hankel matrices of finite rank over the space l of square-summable sequences occur frequently in classical analysis and engineering applications. The notion of finite rank often appears under different contexts and the literature is diverse. The first part of this paper reviews some elegant, classic criteria and establish connections among the various characterizations of...
متن کاملOrthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix ...
متن کاملMatrix Rank Reduction for
Numerical techniques for data analysis and feature extraction are discussed using the framework of matrix rank reduction. The singular value decomposition (SVD) and its properties are reviewed, and the relation to Latent Semantic Indexing (LSI) and Principal Component Analysis (PCA) is described. Methods that approximate the SVD are reviewed. A few basic methods for linear regression, in partic...
متن کاملRank-One Matrix Pursuit for Matrix Completion
Low rank matrix completion has been applied successfully in a wide range of machine learning applications, such as collaborative filtering, image inpainting and Microarray data imputation. However, many existing algorithms are not scalable to large-scale problems, as they involve computing singular value decomposition. In this paper, we present an efficient and scalable algorithm for matrix com...
متن کاملCluster algebras of infinite rank
Holm and Jørgensen have shown the existence of a cluster structure on a certain category D that shares many properties with finite type A cluster categories and that can be fruitfully considered as an infinite analogue of these. In this work we determine fully the combinatorics of this cluster structure and show that these are the cluster combinatorics of cluster algebras of infinite rank. That...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2012
ISSN: 1846-3886
DOI: 10.7153/oam-06-26