Computational details-appendix to the article “Cartan matrices of selfinjective algebras of tubular type”
Computing codimensions and generic canonical forms for generalized matrix products.
Computing exponential for iterative splitting methods: algorithms and applications.
Computing generalized inverse systems using matrix pencil methods
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...
Computing the CS and the Generalized Singular Value Decompositions.
Computing the CS Decomposition of a Partitioned Orthonormal Matrix
Computing the determinantal representations of hyperbolic forms
The numerical range of an matrix is determined by an degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus , and present an elementary computation...
Computing the determinants by reducing the orders by four.
Computing the numerical range of Krein space operators
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Computing tournament sequence numbers efficiently with matrix techniques.
Concentration of the spectral measure for large matrices.
Concentration of the spectral measure for large random matrices with stable entries.
Concentration of the spectral measure of large Wishart matrices with dependent entries.
Concerning Colimits in the Category of Noncommutative Algebras
Concerning row operations on systems of linear equations with integral coefficients.
Condition numbers of Hessenberg companion matrices
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than...
Condition numbers of the Krylov bases and spaces associated with the truncated iteration.
Conditioning properties of the stationary distribution for a Markov chain.
Conditions for a totally positive completion in the case of a symmetrically placed cycle.
Cones of polynomials