We construct the three-variable $p$-adic triple product $L$-functions attached to Hida families of elliptic newforms and prove explicit interpolation formulae at all critical specializations by establishing Ichino's for trilinear period integrals automorphic forms. Our perfectly fit conjectural shape predicted Coates Perrin-Riou. As an application, we factorization certain unbalanced into a ant...

Efficiently solving nonlinear least squares (NLS) problems is crucial for many applications in robotics. In online applications, solving the associated nolinear systems every step may become very expensive. This paper introduces online, incremental solutions, which take full advantage of the sparseblock structure of the problems in robotics. In general, the solution of the nonlinear system is a...

in this paper, we extend some propositions of banachalgebras into module actions and establish the relationships betweentopological centers of module actions. we introduce some newconcepts as                         -property and -property for banach modules and obtain some conclusions inthe topological center of module actions and arens regularity of banachalgebras.

This paper presents the graphical analysis of selection traces in matrix-factorization space of multimedia items. A trace consists of links (lines) between points that present a selected item during interaction between user and video-ondemand (VoD) system. User used gestures to select from among video on screen (VoD service), while additional user-produced social signal (SS) information was use...

We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementa...

This paper presents a class of preconditioning techniques which exploit rational function approximations to the original matrix. The matrix is rst shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner to the original matrix. Since the incomplete factorization is made on a shifted matrix, a good...

The accuracy and effectiveness of matrix factorization technique were well demonstrated in the Netflix movie recommendation contest. Among the numerous solutions for matrix factorization, Stochastic Gradient Descent (SGD) is one of the most widely used algorithms. However, as a sequential approach, SGD algorithm cannot directly be used in the Distributed Cluster Environment (DCE). In this paper...

The efficient solution of large systems of linear equations represented by sparse matrices appears in many tasks. LU factorization followed by backward and forward substitutions is widely used for this purpose. Parallel implementations of this computation-intensive process are limited primarily to supercomputers. New generations of Field-Programmable Gate Array (FPGA) technologies enable the im...

This paper develops a general factorization theory of transfer matrices for linear systems defined over rings. Restricting the rings to the class of unique factorization domains (UFDs) and introducing a notion of denominator sets and a generalized notion of coprimeness, a coprime factorization 1 ( ) ( ) ( ) H z W z V z − = for the transfer matrix ( ) H z of a system defined over a UFD is develo...

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein–Vandermonde matrix is considered. Bernstein–Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...