Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the s...

The problem of outliers is well-known in statistics: an outlier is a value that is far from the general distribution of the other observed values, and can often perturb the results of a statistical analysis. Various procedures exist for identifying outliers, in case they need to receive special treatment, which in some cases can be exclusion from consideration. An inlier, by contrast, is an obs...

The tensor M has 3 = 81 entries and no symmetries. Both the construction and application of M are somewhat expensive, and both can be avoided. If F = UΣV , then it turns out that Z(F, α) = UẐ(Σ, α)V and W(F) = UŴ(Σ)V , where Ẑ(Σ, α) and Ŵ(Σ) are diagonal matrices. It follows then that Y(F) = UŶ(Σ)V , with Ŷ(Σ) = Ŵ(Ẑ(Σ, α)), where Ŷ(Σ) is also a diagonal matrix. To be able to carry out these ste...

The tensor M has 3 = 81 entries and no symmetries. Both the construction and application of M are somewhat expensive, and both can be avoided. If F = UΣV , then it turns out that Z(F, α) = UẐ(Σ, α)V and W(F) = UŴ(Σ)V , where Ẑ(Σ, α) and Ŵ(Σ) are diagonal matrices. It follows then that Y(F) = UŶ(Σ)V , with Ŷ(Σ) = Ŵ(Ẑ(Σ, α)), where Ŷ(Σ) is also a diagonal matrix. To be able to carry out these ste...

SUBTITLE. Despite its important signal processing applications, the generalized singular value decomposition (GSVD) is under-utilized due to the high updating cost. In this paper, we introduce a new approximate GSVD that is easily amenable to updating. ABSTRACT. To solve the noise subspace problem, we extend the generalized singular value decomposition to a new decomposition that can be updated...

An image watermarking scheme based on singular value decomposition and visual cryptography in discrete wavelet transform is proposed. We start with a survey of the current image watermarking technologies, and have noticed that majority of the existing schemes are not capable of resisting all attacks. We propose the idea to use of singular value decomposition and visual cryptography in discrete ...

Collaborative Filtering is effective to provide customers with personalized recommendations by analyzing the purchase pattens. Matrix factorization, e.g. Singular Value Decomposition, is another successful technique in recommendation system. We implemented Singular Value Decomposition algorithm to achieve the least total squared errors. Based on the result, item-feature Collaborative Filtering ...

This note is intended to summarize the definition, properties, interpretation and applications of Singular Value Decomposition (SVD) described by Strang [?], Shilov [?], Johnson and Wichern [?] and Will [?]. 1 Definition Singular Value Decomposition (SVD) technique decomposes a m × n matrix A into the following factored form :

In the first part of the paper we prove that for 2 < p, r < ∞ every operator T : Lp → lr is narrow. This completes the list of sequence and function Lebesgue spaces X with the property that every operator T : Lp → X is narrow. Next, using similar methods we prove that every l2-strictly singular operator from Lp, 1 < p < ∞, to any Banach space with an unconditional basis, is narrow, which partia...