We study k-GenEV, the problem of finding the top k generalized eigenvectors, and k-CCA, the problem of finding the top k vectors in canonicalcorrelation analysis. We propose algorithms LazyEV and LazyCCA to solve the two problems with running times linearly dependent on the input size and on k. Furthermore, our algorithms are doubly-accelerated: our running times depend only on the square root ...

The polar decomposition of an m x n matrix A of full rank, where rn n, can be computed using a quadratically convergent algorithm of Higham SIAMJ. Sci. Statist. Comput., 7 (1986), pp. 1160-1174]. The algorithm is based on a Newton iteration involving a matrix inverse. It is shown how, with the use of a preliminary complete orthogonal decomposition, the algorithm can be extended to arbitrary A. ...

Square root plays a major role in applications like computer graphics, image processing. To increase the performance of computation, many algorithms have been proposed to carry out the computation task in hardware instead of software. One very common and relatively quick method for finding the square root of a number is the Newton-Raphson method which requires extensive use of division to produ...

We discuss methods for time-discretization and simulation of squareroot SDEs, both in isolation (CIR process) and as part of vector-SDEs modeling stochastic volatility (Heston model). Both exact and biased discretization methods are covered.

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the roundoff errors, in the case of the small value of the observation noise va...

The spectra of self-adjoint operators in Krein spaces are known to possess real sectors as well as sectors of pair-wise complex conjugate eigenvalues. Transitions from one spectral sector to the other are a rather generic feature and they usually occur at exceptional points of square root branching type. For certain parameter configurations two or more such exceptional points may happen to coal...

Cholesky factorization is the computationally most expensive step in numerically solving positive definite systems. Due to inherently recursive computation process and associated floating point division and square root operations in Cholesky factorization, it is very difficult to obtain acceleration by exploiting parallelism on FPGA’s. To solve this problem, approach suggests iterative architec...