Vance Faber

Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method

We characterize the class

An Upper Bound on the Diameter of a Graph from Eigenvalues Associated with its Laplacian

CG(s)

Algebraic Constructions of Efficient Broadcast Networks

of matrices A for which the linear system

Cycle prefix digraphs for symmetric interconnection networks

A{\bf x} = {\bf b}

The Degree-Diameter Problem for Several Varieties of Cayley Graphs I: The Abelian Case

can be solved by an s-term conjugate gradient method. We show that, except for a few anomalies, the class

Orthogonal error methods

CG(s)

Minimal Residual Method Stringer than Polynomial Preconditioning

consists of matrices A for which conjugate gradient methods are already known. These matrices are the Hermitian matrices,

Small diameter symmetric networks from linear groups

A^ * = A

Modeling the performance of hypercubes: A case study using the particle-in-cell application

, and the matrices of the form

Reflected boundary conditions for multirate filter banks

Ae^{i\theta} (dI + B)