Showing papers in "Linear Algebra and its Applications in 1989"

TL;DR: Finite and iterative methods are given, based on results from linear complementarity theory, for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right-hand sides vary in some real intervals.

TL;DR: In this article, the authors introduce the notion of Doubly Stochastic Matrices (DSM) and compare its properties with those of other matrices with minimum permanent and double sub-and superstochasticity.

TL;DR: This work investigates two different variants of relaxed multisplitting methods, if A is an H-matrix, these methods converge if the relaxation parameter is from an interval (0,ω0) with ω0 > 1.

TL;DR: For positive two-dimensional matrices, Hilbert's projective metric and a theorem of G. Birkhoff are used to prove that Sinkhorn's original iterative procedure converges geometrically; the ratio of convergence is estimated from the given data as discussed by the authors.

TL;DR: A class of algorithms for the generation of curves and surfaces encompass some well-known methods of subdivision for Bernstein-Bezier curves and B -spline curves and Lane and Riesenfeld's algorithm is proposed.

TL;DR: In this article, a block-iterative version of the Agmon-Motzkin-Schoenberg relaxation method for solving systems of linear inequalities is derived, and it is shown that any sequence of iterations generated by the algorithm converges if the intersection of the given family of convex sets is nonempty and that the limit point of the sequence belongs to this intersection under mild conditions on the sequence of weight functions.

TL;DR: In this article, the authors considered the problem of computing an x such that an x = t such that ==================¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−1−1, −1.

TL;DR: It is shown that the Chebyshev error bound holds (to a close approximation) for slightly perturbed conjugate-gradient recurrences, and that a sharper error bound can be expressed in terms of the minimax polynomial on a set of small intervals about the eigenvalues of the matrix.

TL;DR: In this article, it was shown that the norms of both matrices are bounded by numbers that are independent of the positive diagonal elements of the matrix and the oblique projection of the diagonal matrix.

TL;DR: In this article, the authors consider the problem of finding a permutation group on n letters in the orthogonal group O ( n ) with the latter acting on R n (n + 1)/2 via a symmetricized tensor product.

TL;DR: In this article, it was shown that the closure of the set of all representations with properties (a) and (b) is irreducible as an algebraic variety.

TL;DR: In this paper, the authors introduce the class of column sufficient matrices, which are the transpose of a matrix M such that for every vector q, the solutions of the linear complementarity problem are identical to the Karush-Kuhn-Tucker points associated with ( q, M ).

TL;DR: Barahona, Grotschel, and Mahjoub as mentioned in this paper proved that polyhedra featured in popular formulations of the stable-set problem, the set-covering problem, set-partitioning, knapsack problem, bipartite-subgraph problem, maximum-cut problem, acyclic-subdigraph problem, asymmetric traveling-salesman problem, and the traveling salesman problem have arbitrarily high rank.

TL;DR: In this paper, a new framework for problems concerning supermodular functions and graphs is introduced, which is an optimization problem for finding a minimum-cost subgraph H of a digraph G = V, E such that H contains k disjoint paths from a fixed path from a node of G to any other node.

TL;DR: It is shown that the smallest singular value of A is bounded below by min 1 ⩽i⩽N, which improves upon two known lower bounds without increasing information requirements or complexity of calculation.

TL;DR: In this article, a complete description of determinantal representations of smooth irreducible curves over any algebraically closed field is presented. Butler et al. used the notion of the class of divisors of the vector bundle corresponding to a determinant-al representation; they proved that two determinant representations of a smooth curve F are equivalent if and only if the classes of the corresponding vector bundles coincide.

TL;DR: A new way of introducing invariant subspaces for generalized systems is presented, from somewhat known geometric algorithms but, in most cases, with initial conditions different from those usually seen in this context.

TL;DR: In this paper, a novel approach is followed, using the singular-value, generalized singular value, real Schur, and real generalized Schur decomposition, and the numerical properties of the related solution procedures are discussed briefly.

TL;DR: In this article, necessary and sufficient conditions are given for the existence of a feedback which assigns the maximum possible number of finite poles with regularity and maximum robustness in a closed-loop semistate system.

TL;DR: In this paper, the authors initiated the study of GCD matrices in the direction of their structure, determinant, and arithmetic in Z n. Several open problems are posed.

TL;DR: In this article, the authors considered the problems of inheriting certain properties under a given ordering, preserving an ordering under some matrix multiplications, relationships between an ordering among direct (or Kronecker) and Hadamard products and the corresponding orderings between the factors involved, and ordering between generalized inverses of a given matrix.

TL;DR: For a nonnegative irreducible matrix A with spectral radius ϱ, the determination of the unique normalized Perron vector π which satisfies A π = ϱπ, π #&62; 0, Σ j π j = 1 was studied in this article.

TL;DR: The problem of scaling a matrix so that it has given row and column sums is transformed into a convex minimization problem and this transformation is used to characterize the existence of such scaling or corresponding approximations.

TL;DR: In this article, rank-one updates to improve H as an approximation to A−1 during the iteration were discussed, and the update kills and reduces singular values of I − AH and thus speeds up the convergence.

TL;DR: In this article, the notion of Euclidean t-design is analyzed in the framework of appropriate inner product spaces of polynomial functions, and Fisher type inequalities are obtained in a simple manner by this method.

TL;DR: In this article, Riccati balanced coordinates are derived for the set of minimal systems of given order from a canonical form for a class of coinner transfer functions and applied to model reduction.

TL;DR: In this paper, the mixed discriminant can be expressed as an inner product and a Ryser-type formula for it is given for a generalization of Konig's theorem on 0-1 matrices.

TL;DR: The authors complete the determination of the graphs in the title, begun by Cvetkovic, Doob, and Gutman, and show that they are the same graphs as the ones in this paper.

TL;DR: In this paper, it was shown that a positive function ǫ(t) is m.m.m iff t ƒ(t), t is strictly convex.

TL;DR: In this paper, an explicit determinantal formula for the (unique) determinant-maximizing positive definite completion (maximum entropy completion) of a chordal graph is given.