A CMV-Based Eigensolver for Companion Matrices

Lightweight 4x4 MDS Matrices for Hardware-Oriented Cryptographic Primitives

Linear diffusion layer is an important part of lightweight block ciphers and hash functions. This paper presents an efficient class of lightweight 4x4 MDS matrices such that the implementation cost of them and their corresponding inverses are equal. The main target of the paper is hardware oriented cryptographic primitives and the implementation cost is measured in terms of the required number ...

Compression of unitary rank-structured matrices to CMV-like shape with an application to polynomial rootfinding

This paper is concerned with the reduction of a unitary matrix U to CMV-like shape. A Lanczos–type algorithm is presented which carries out the reduction by computing the block tridiagonal form of the Hermitian part of U , i.e., of the matrix U +UH . By elaborating on the Lanczos approach we also propose an alternative algorithm using elementary matrices which is numerically stable. If U is ran...

Toward High Performance Divide and Conquer Eigensolver for Dense Symmetric Matrices

This paper presents a high performance eigensolver for dense symmetric matrices on multicore architectures. Based on the well-known divide and conquer (D&C) methodology introduced by Cuppen, this algorithm computes all the eigenvalues of the symmetric matrix. The general D&C can be expressed in three stages: (1) Partitioning into subproblems, (2) Computing the solution of the subproblems and (3...

Darboux transformations for CMV matrices

We develop a theory of Darboux transformations for CMV matrices, canonical representations of the unitary operators. In perfect analogy with their self-adjoint version – the Darboux transformations of Jacobi matrices – they are equivalent to Laurent polynomial modifications of the underlying measures. We address other questions which emphasize the similarities between Darboux transformations fo...

A Robust Eigensolver for 3× 3 Symmetric Matrices