This dissertation is located in the field of numerical linear algebra. It proposes algorithms for
solving structured eigenvalue problems arising in electronic structure computations …

The paper describes several efficient parallel implementations of the one-sided hyperbolic
Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By …

Let A be a Hermitian positive definite matrix given by its rectangular factor G such that A= G*
G. It is well known that the Cholesky factorization of A is equivalent to the QR factorization of …

It is well known that orthogonalization of column vectors in a rectangular matrix B with
respect to the bilinear form induced by a nonsingular symmetric indefinite matrix A can be …

We present methods for computing the generalized polar decomposition of a matrix based
on the dynamically weighted Halley iteration. This method is well established for computing …

We develop a general theory of reflectors and block reflectors in a class of non-Euclidean
scalar product spaces generated by orthosymmetric scalar product matrices J. These J …

We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with
respect to a given indefinite scalar product (ie, pseudosymmetic matrices). The …

To compute the eigenvalues of a skew-symmetric matrix A, we can use a one-sided Jacobi-
like algorithm to enhance accuracy. This algorithm begins by a suitable Cholesky-like …

The hyperbolic QR factorization is a generalization of the classical QR factorization and can
be regarded as the triangular case of the indefinite QR factorization proposed by Sanja …

This thesis is motivated by a problem that is a generalization of the linear least squares (LS)
problem minx (b-Ax) T (b-Ax). The indefinite least squares (ILS) problem is to solve …