On normal and structured matrices under unitary structure-preserving transformations

Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing those canonical forms is sketched.Comment: The original submission is split into two parts. The manuscript submitted here deals only with the derivation of structured canonical forms for normal structured matrices. 15 pages, 2 figure

A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process

We discuss a Krylov-Schur like restarting technique applied within the symplectic Lanczos algorithm for the Hamiltonian eigenvalue problem. This allows to easily implement a purging and locking strategy in order to improve the convergence properties of the symplectic Lanczos algorithm. The Krylov-Schur-like restarting is based on the SR algorithm. Some ingredients of the latter need to be adapted to the structure of the symplectic Lanczos recursion. We demonstrate the efficiency of the new method for several Hamiltonian eigenproblems

Structured Eigenvalue Problems

Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may improve the accuracy and efficiency of an eigenvalue computation. The purpose of this brief survey is to highlight these facts for some common matrix structures. This includes a treatment of rather general concepts such as structured condition numbers and backward errors as well as an overview of algorithms and applications for several matrix classes including symmetric, skew-symmetric, persymmetric, block cyclic, Hamiltonian, symplectic and orthogonal matrices

7th Workshop on Matrix Equations and Tensor Techniques

No abstract availabl

Intracellular APP Domain Regulates Serine-Palmitoyl-CoA Transferase Expression and Is Affected in Alzheimer's Disease

Lipids play an important role as risk or protective factors in Alzheimer's disease (AD), a disease biochemically characterized by the accumulation of amyloid beta peptides (Aβ), released by proteolytic processing of the amyloid precursor protein (APP). Changes in sphingolipid metabolism have been associated to the development of AD. The key enzyme in sphingolipid de novo synthesis is serine-palmitoyl-CoA transferase (SPT). In the present study we identified a new physiological function of APP in sphingolipid synthesis. The APP intracellular domain (AICD) was found to decrease the expression of the SPT subunit SPTLC2, the catalytic subunit of the SPT heterodimer, resulting in that decreased SPT activity. AICD function was dependent on Fe65 and SPTLC2 levels are increased in APP knock-in mice missing a functional AICD domain. SPTLC2 levels are also increased in familial and sporadic AD postmortem brains, suggesting that SPT is involved in AD pathology

On numerical methods for discrete least-squares approximation by trigonometric polynomials

Abstract. Fast, efficient and reliable algorithms for discrete least-squares approximation of a real-valued function given at arbitrary distinct nodes in [0, 2π) by trigonometric polynomials are presented. The algorithms are based on schemes for the solution of inverse unitary eigenproblems and require only O(mn) arithmetic operations as compared to O(mn 2) operations needed for algorithms that ignore the structure of the problem. An algorithm which solves this problem with real-valued data and real-valued solution using only real arithmetic is given. Numerical examples are presented that show that the proposed algorithms produce consistently accurate results that are often better than those obtained by general QR decomposition methods for the least-squares problem. 1