Differential Riccati equations are at the heart of many applications in control theory. They time-dependent, matrix-valued, and particular nonlinear that require special methods for their solution. Low-rank have been used heavily computing a low-rank solution every step time-discretization. We propose use an all-at-once space-time leading to large problem which we Newton–Kleinman iteration. App...

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank, and in practice, these methods are effective even for high-dimensional datasets. The practical success has elicited the theoretical analysis of the function rank in this paper, which is an upper bound of...

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptions about the data, e.g., low rank of the data matrix or a large separable mar...

Abstract In this paper we study the convergence of the well-known Greedy RankOne Update Algorithm. It is used to construct the rank-one series solution for fullrank linear systems. The existence of the rank one approximations is also not new, but surprisingly the focus there has been more on the applications side more that in the convergence analysis. Our main contribution is to prove the conve...

Article history: Received 31 October 2011 Accepted 15 May 2012 Available online 28 June 2012 Submitted by Volker Mehrmann AMS classification: 15A60 15B48 15A03

The many advantages of renewable energies—especially wind—such as abundance, permanence, and lack of pollution, have encouraged many industrialized and developing countries to focus more on these clean sources of energy. The purpose of this study is to prioritize and rank 13 cities of the Fars province in Iran in terms of their suitability for the construction of a wind farm. Six important ...

Today, compact and reduced data representations using low rank data approximation are common to represent high-dimensional data sets in many application areas as for example genomics, multimedia, quantum chemistry, social networks or visualization. In order to produce such low rank data representations, the input data is typically approximated by so-called alternating least squares (ALS) algori...