Showing papers in "Linear Algebra and its Applications in 1984"

TL;DR: In this article, it was shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of the specified entries is chordal, a positive definite completion necessarily exists.

TL;DR: A new class of algorithms which is based on rational functions of the matrix is described, and there are also new algorithms which correspond to rational functions with several poles.

TL;DR: An error analysis of the symmetric Lanczos algorithm in finite precision arithmetic shows that semiorthogonality among the Lanczos vectors is enough to guarantee the accuracy of the computed quantities up to machine precision.

TL;DR: In this paper, the spectral properties of the iteration matrix M-1N were investigated by considering the relationships of the graphs of A, M, N, and M 1 n for an irreducible Z-matrix A, and it was shown that the circuit index of M -1N is the greatest common divisor of certain sets of integers associated with the circuits of A.

TL;DR: In this paper, a computable criterion for two square matrices to possess a common eigenvector, as well as a criterion for one matrix to have an eigen vector lying in a given subspace are discussed.

TL;DR: The new concept of a sublinear map, coupled with a systematic use of Ostrowski's comparison operator, is used to derive quantitative information about the result of interval Gauss elimination and the limit of various iterative schemes for the solution of linear interval equations.

TL;DR: For the pair of matrix equations AX = C, XB = D, the authors gives common solutions of minimum possible rank and also other feasible specified ranks and also provides a feasible specified rank.

TL;DR: In this article, the location and multiplicity of eigenvalues of sign symmetric matrices whose associated graphs are trees are investigated. But the results are restricted to the case of trees.

TL;DR: In this article, the authors studied the extent to which certain theorems on linear operators on field-valued matrices carry over to linear operations on Boolean matrices and obtained analogues and near analogues of several such theoresms.

TL;DR: In this paper, it was shown that general linear matrix equations with block-companion matrix coefficients can be transformed to equations whose coefficients are block companion matrices: C L X−XC M = diag [I 0…0] and X−C L XC M= diag[I 0..0], respectively, where ĈL and CM stand for the first and second blockcompanion matrices of some monic r × r matrix polynomials L(λ) = λsI + Σs−1j=0

TL;DR: In this article, the convexity of the numerical range has been shown for any n-dimentional unitary space with inner product (·,·) and the set W(A:q) = tr (CU ∗ AU):U unitary where C∈Hom(V, V).

TL;DR: Various forms of preconditioning matrices for iterative acceleration methods are discussed, based on two versions of incomplete block-matrix factorization.

TL;DR: In this article, the mutual relations between the Hankel, Toeplitz, Bezout, and Loewner matrices as well as further connections to rational interpolation and projective geometry are investigated.

TL;DR: In this article, simple estimation theorems for singular values of a rectangular matrix A are given, and a bound for the condition number of A may be obtained from them, which explains why scaling improves the performance of Gauss elimination when row or column norms differ widely in magnitude.

TL;DR: In this article, the Schur complement theory is used for the derivation of criteria for the definiteness of the restriction of a quadratic form to the null space of a matrix.

TL;DR: In this article, the authors study stability of subspaces which are invariant under a self-adjoint matrix in an indefinite inner product, and have various maximality and semidefinite properties with respect to this inner product.

TL;DR: New results are obtained, giving the exact convergence and divergence domains for such iterative applications of the block-SOR iterative method to a consistently ordered block-Jacobi matrix that is weakly cyclic of index 3.

TL;DR: In this paper, four different measures of inefficiency of the simple least squares estimator in the general Gauss-Markoff model are considered, and new bounds are obtained for a particular measure.

TL;DR: In this paper, Richardson's iteration (2) x j + 1 = x j -α j (Ax j -a ), j = 1,2,…, n, which is applied in a cyclic manner with cycle length n is investigated, where the α j are free parameters.

TL;DR: It is shown that there are exactly n distinct smooth curves connecting trivial solutions to desired eigenpairs and these curves are solutions of a certain ordinary differential equation with different initial values.

TL;DR: In this article, a new method is presented for the solution of the matrix eigenvalue problem Ax=λBx, where A and B are real symmetric square matrices and B is positive semidefinite.

TL;DR: It is proved that homodual method converges when one of the norms φ and ψ is polyhedral.

TL;DR: This functional equation is applied to the problem of determining bounds for the intervals of convergence and divergence of the SSOR iterative method for classes of H -matrices.

TL;DR: The singular pairs of n × n matrices [those satisfying det( A − λB )  0] form a closed set of codimension n + 1 inside the space of all matrix pairs as mentioned in this paper.

TL;DR: In this article, the authors obtained eigenvalue bounds for pencils of matrices A − vB where A is a Stieltjes matrix and B is positive definite, under assumptions suitable for the estimation of asymptotic convergence rates of factorization iterative methods.

TL;DR: In this paper, a necessary and sufficient condition for the sequence { A k} of the powers of an interval matrix A to converge to the null matrix O is given, and a point matrix B which has spectral radius ϱ (B ) less than one if A k converges is constructed.

TL;DR: In this paper, an expansion for the square of the smallest singular value of a matrix is presented, and the expansion includes second order terms in the pertubation and therefore remains accurate when the largest singular value is zero.

TL;DR: In this article, a computational method for dealing with a class of matrices which arise in quantum mechanics involving time reversal and inversion symmetry is described, which greatly reduces the computational effort required to solve this problem and also produces a stable, more accurate solution.

TL;DR: In this paper, explicit forms for orgodicity coefficients which bound the non-unit eigenvalues of finite stochastic matrices are known in the cases p = 1, ∞ when the lp norm is used.

TL;DR: In this paper, Bapat applied a topological theorem of Kronecker and generalized a theorem of Sinkhorn on positive matrices and gave an alternative proof of a slightly stronger version of his generalization.