‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

The problem of matrix inversion is central to many applications of Numerical Linear Algebra. When the matrix to invert is dense, little can be done to avoid the costly O(n) process of Gaussian Elimination. When the matrix is symmetric, one can use the Cholesky Factorization to reduce the work of inversion (still O(n), but with a smaller coefficient). When the matrix is both sparse and symmetric...

In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...

The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. The result is derived by using the construction given in [1], where the Ruijsenaars operator was obtained as the transfer matrix associated to the symmetric power of the vector representation of the elliptic quantum group Eτ,γ(glN ).

The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in ...

The action of a subgroup G of automorphisms of a graph X is said to be 2 -transitive if it is vertexand edgebut not arc-transitive. In this case the graph X is said to be (G, 2)-transitive. In particular, X is 1 2 -transitive if it is (Aut X, 1 2)-transitive. The 2 -transitive action of G on X induces an orientation of the edges of X which is preserved by G. Let X have valency 4. An even length...