A novel parallel formulation of Hessenberg-triangular reduction of a regular matrix pair on distributed memory computers is presented. The formulation is based on a sequential cache-blocked algorithm by Kågström, Kressner, E.S. Quintana-Ortí, and G. QuintanaOrtí (2008). A static scheduling algorithm is proposed that addresses the problem of underutilized processes caused by two-sided updates of...

The rational Krylov sequence (RKS) method is a generalization of Arnoldi's method. It constructs an orthogonal reduction of a matrix pencil into an upper Hessenberg pencil. The RKS method is useful when the matrix pencil may be eeciently factored. This article considers approximately solving the resulting linear systems with iterative methods. We show that a Cayley transformation leads to a mor...

In this paper we propose design of three systolic arrays to perform QR decomposition of a square matrix. Our first design is based on Given’s rotation method [1]. In contrast to the earlier designs [1], [2] based on this method, our design uses n(n − 1)/2 homogeneous PEs. Our next design is based on Householder method [4]. This method performs only (n− 1) square root operations in contrast to n...

We present methods for improving data reuse in solving sequences of linear systems that are Hessenberg matrices shifted by a sequence of scalars times the identity or a triangular matrix. The methods take into consideration the robust handling of overrow and include new condition estimation strategies. We provide timings on both scalar and vector machines to demonstrate both the diversity and i...

Practical QR algorithm for the real unsymmetric algebraic eigenvalue problem is considered. The global convergence of shifted QR algorithm in finite precision arithmetic is addressed based on a model of the dynamics of QR algorithm in a neighborhood of an unreduced Hessenberg fixed point. The QR algorithm fails at a “stable” unreduced fixed point. Prior analyses have either determined some unst...

Thompson’s partition of a cyclic subnormal operator into normal and completely non-normal components is combined with non-commutative calculus for hyponormal operators separating outliers from the cloud, in rather general point distributions plane. The main result provides exact transformation formulas power moments prescribed distribution uniform mass carried by cloud. proposed algorithm solel...

Watermarking is a valuable technique for verifying medical images obtained through the internet diagnosis. There greater need security in pictures with ever- increasing risks. This research presented Finite Ridgelet Transform (FRT)-Hessenberg based watermarking scheme images. The suggested paradigm divided into two stages. Before watermark insertion, FRT applied to coefficients are combined blo...

This paper considers the maximum value of the permanent over the class H(m, n) of n × n Hessenberg, (0, 1)-matrices with m 1’s, and shows that among those matrices that attain the maximum value there exists a matrix with a special form. This special form determines the exact value of the maximum permanent on H(m, n) for certain values of m and n.