We present a fast algorithm for approximate canonical correlation analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input matrices, and then applies any CCA algorithm to the new pair of matrices. The algorithm computes an approximate CCA to the original pair of matrices with prov...

Rotating beams have been considerably appealing to engineers and designers of complex structures i.e. aircraft’s propeller and windmill turbines. In this paper, a new flexibility-based method is proposed for the dynamic analysis of rotating non-prismatic Euler-Bernoulli beams. The flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the...

Here we consider a class of 2⊗ 2⊗ d chessboard density matrices starting with threequbit ones which have positive partial transposes with respect to all subsystems. To investigate the entanglement of these density matrices, we use the entanglement witness approach. For constructing entanglement witnesses (EWs) detecting these density matrices, we attempt to convert the problem to an exact conve...

Approximation of matrices using the Singular Value Decomposition (SVD) plays a central role in many science and engineering applications. However, the computation cost of an exact SVD is prohibitively high for very large matrices. In this paper, we describe a GPU-based approximate SVD algorithm for large matrices. Our method is based on the QUIC-SVD introduced by [6], which exploits a tree-base...

An exact formula was recently obtained for the spectral norms of the Lucas and Fibonacci Hankel matrices [1], and also for the Lucas and Fibonacci Toeplitz matrices [4]. These results put finishing touches on the works initiated in [2] and [3]. On another front, bounds were found for the spectral norms of k-Fibonacci and k-Lucas Toeplitz matrices [7]. In this paper, we present the exact value f...

A novel element with arbitrary domain shape by using decoupled scaled boundary finite element (DSBFEM) is proposed for eigenvalue analysis of 2D vibrating rods with different boundary conditions. Within the proposed element scheme, the mode shapes of vibrating rods with variable boundary conditions are modelled and results are plotted. All possible conditions for the rods ends are incorporated ...

For the nonlinear analysis of structures using the well known Newton-Raphson Method, the tangent stiffness matrices of the elements must be constructed in each iteration. Due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the Newton-Raphson method to reduce the cost and time required by the analysis. In this paper, a ...

and Applied Analysis 3 The vector representation of the above-mentioned truncated series can be written in the following form: y N (t)