Showing papers in "Linear Algebra and its Applications in 1986"

TL;DR: For a nonnegative matrix P, the relation of its marked reduced graph to that part of the Jordan form associated with the Perron-Frobenius root is discussed in this paper.

TL;DR: Two algorithms are presented which determine rank and nullity in a numerically stable manner without using column interchanges and one makes use of the condition estimator of Cline, Moler, Stewart, and Wilkinson and relative to alternative stable algorithms is particularly efficient for sparse matrices.

TL;DR: A set of procedures for computing and updating an LU factorization of a sparse matrix A, where A may be square (possibly singular) or rectangular, and rank-one modification, lower and upper triangular is described.

TL;DR: In this article, the spectral radius of a nonnegative matrix is shown to be a convex function of the diagonal elements of the matrix, and a generalization of Kingman's theorem to a subclass of nonlinear maps is given.

TL;DR: Schur complements as discussed by the authors are matrices of the form S = D − CaB, where a is a generalized inverse of A, and are the matrices for which the Schur complement of A in M = A B C D is the same as A in C D.

TL;DR: A Jacobi-type algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form, which can be extended to a “rectangular” one with 12mn + O(m) processors for the computational of singular vectors.

TL;DR: In this article, the authors studied the use of unitary unitary similarity transformations in the QR decomposition, where S is either unitary or unitary symplectic, respectively.

TL;DR: In this article, the sensitivity of stationary distribution vectors p/sup infinity/ to perturbations in the transition probabilities of Markov chains with associated transition matrices T is analyzed. But the sensitivity is not limited to the case where there is a state that is accessible from every other state and T has no small off-diagonal elements.

TL;DR: A parallel algorithm is developed for Cholesky factorization on a shared-memory multiprocessor based on self-scheduling of a pool of tasks and the most promising variant, which the authors call column-Cholesky, is identified and implemented for the Denelcor HEP multiproprocessor.

TL;DR: In this article, necessary and sufficient conditions are given for the triple reverse order law (ABC) = C†B†A† to hold, and special cases are considered for some special cases.

TL;DR: In this paper, the nullities of A 11 and B 22 are shown to be equal in terms of the order p × q of the transposed partitioning B 11 B 12 B 21 B 22.

TL;DR: In this article, a unified algorithm of order N2 for N×N matrices with recursive structure is presented. And several known algorithms as well as some new ones for Toeplitz type, Hilbert type, and Vandermonde type matrices are given.

TL;DR: The main result of as mentioned in this paper is that Drazin's "star" partial ordering holds if and only if A ∠ B and B −A −A =(B−A)

TL;DR: In this paper, the maximum number of nonzero elements in square L-matrices is determined, and it is shown that for any n×n l-matrix there is an i such that the total number of n nonzero entries in the ith row and ith column is less than n unless the matrix has a completely specified structure.

TL;DR: In this article, a lower bound for arbitrary matrices (with nonnegative entries) acting on arbitrary l p spaces, 1⩽ p ⩽∞, was established.

TL;DR: Some existence results for methods based on the approximate factorization of block matrices are proven and a recently proposed inverse free factorization method is discussed.

TL;DR: The method generalizes previous methods for pointwise incomplete factorization as well as a method for tridiagonal block matrices and presents a new and more general result on the existence of so-called modified incomplete factorizations which satisfy a generalized rowsum criterion.

TL;DR: This paper shows how to compute a stable decomposition of an uncertain matrix T which varies continuously and boundedly as T varies in a ball of radius ϵ.

TL;DR: In this article, finite criteria for copositive matrices are proposed and compared with existing determinantal tests, including principal pivoting and principal pivot-based matrices, and the basic mathematical tool is principal pivot.

TL;DR: The definition of the shorted matrix given in this paper is similar to the Krein-Anderson-Trapp definition of shorted positive operator, which is used to define the infimum A ∧ B and the supremum A ∨ B of a pair A, B of matrices of the same order.

TL;DR: In this article, a general matrix expression for the asymptotic covariance matrix of correlation coefficients is derived for data drawn from any distribution with finite fourth order moments, which is applicable to the cases where the data have a distribution from the elliptical class and the sample covariance has a noncentral Wishart distribution.

TL;DR: In this article, it was shown that the cyclic Kogbetliantz algorithm ultimately converges quadratically when no pathologically close singular values are present, where singular values can be defined.

TL;DR: In this paper, two theorems on the canonical Kronecker form of a perturbed matrix pencil and the characterization of the closure of the set of all matrix pencils with a fixed canonical form are given.

TL;DR: The objective is to compare a variety of algorithms, which are fairly reasonable to program and to analyze, for the solution of a single problem on a certain class of parallel architectures, thereby leading to a more realistic approach to future algorithm development on multiprocessor machines.

TL;DR: In this paper, a positive linear map from M 2 to M 4 which is not decomposable was shown to be a counterexample to a conjecture of Woronowicz on the strong Kadison inequality.

TL;DR: A few lower bounds for communication complexity of the Gaussian elimination algorithm on multiprocessors are proposed, showing that for the bus and the ring architectures, the minimum communication time is O(N2), independent of the number of processors.

TL;DR: In this article, the Radon-Nikodym property of Banach spaces has been shown to be equivalent to Bourgain's theorem of Bourgain in terms of optimization results, and some old ideas of Smulian can be used to give another proof of a theorem.

TL;DR: For monotone matrices and H -matrices, maximum principles are defined, and necessary and sufficient conditions are derived for these principles to hold as discussed by the authors. But the maximum principles do not hold for H-matrices.

TL;DR: Modifications to many of the standard algorithms used in computing eigenvalues and eigenvectors of matrices can dramatically increase the performance of the underlying software on high-performance computers without resorting to assembler language.

TL;DR: In this article, the authors developed some techniques for estimating the maximal dimension of a linear subspace V of L (C n, C m ) such that every nonzero map in V has rank k.