Showing papers in "Linear Algebra and its Applications in 1983"

TL;DR: In this article, the concepts of strong detectability and strong observability for continuous-time systems are studied and conditions for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state.

TL;DR: This paper takes a unified approach to the partial realization problem in which it seeks to incorporate ideas from numerical linear algebra, most of which were originally developed in other contexts.

TL;DR: The typical rank (= maximal border rank) of tensors of a given size and the set of optimal bilinear computations of typical TensorRank are investigated and it is shown that for the size ( n, n, 3) with n odd, the complement of theSet of Tensors of maximal borderRank is a hypersurface.

TL;DR: In this paper, the general continuous-time linear-quadratic control problem is considered, and it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem.

TL;DR: Two algorithms, based on the bisection technique and Newton's method, are shown to be very fast for computing the eigenvalues of a 7− or 5-diagonal BST-matrix.

TL;DR: The method is based on the Schur factorization A = QSQ H and uses a fast recursion to compute the upper triangular square root of S and it is shown that if α = ∥ X ∥ 2 /∥ A ∥ is not large, then the computed square root is the exact square root

TL;DR: In this article, it was shown that the spectrum of B can be obtained from that of A (multiplicities counted) by moving each eigenvalue by at most ϵ.

TL;DR: In this article, the zero structure, the polar structure, and the left and right null space structure of a polynomial matrix P(λ) have been computed using a new numerical method.

TL;DR: In this article, the authors give a formal treatment of determinantal identities of the minors of a matrix and give a common, concise derivation of some important determinantial identities attributed to the mathematicians in the title.

TL;DR: In this paper, the authors study spaces generated by translations of a fixed function over lattice points and provide algebraic and approximation properties for these spaces which show their applicability for finite element analysis.

TL;DR: Various representations for systems described by aset of high-order differential equations of the form R0w + R1w + … + Rsw(s) = 0, with R0, R1,…, Rs not necessarily square matrices are developed.

TL;DR: In this article, a criterion for copositive matrices is given and for n = 3 the set of all copositives is determined in terms of matrix elements, and the problem of excluding periodic solutions of certain algebraic differential equations is considered.

TL;DR: A unifying framework is revealed where several known results fit naturally and special attention is given to the embedding problem of the Lyapunov equation in view of its direct application to generalized Levinson algorithms.

TL;DR: In this article, a detailed study of symmetric transfer functions is presented, and a detailed analysis of transfer functions can be found in Section 5.1.1]...

TL;DR: In this paper, a class of special, highly efficient multigrid methods for solving h-discrete elliptic differential equations is introduced, which are characterized by intermediate grids (between the given h-grid and the 2h-grid) and by special fine-to-coarse and coarse-tofine grid transfer techniques.

TL;DR: Several variants of Gram-Schmidt orthogonalization are reviewed from a numerical point of view in this paper, and it is shown that the classical and modified variants correspond to the Gauss-Jacobi and Gauss -Seidel iterations for linear systems.

TL;DR: In this article, it was shown that the generalized conjugate-gradient (CC) can be simplified if a nonsingular matrix H is available such that HA = ATH.

TL;DR: In this article, the condition number of the n X n matrix p = [Pi-ltxj)lY,Y,j-l is investigated, where p,((.) = p, (.; dX) are orthogonal polynomials with respect to some weight distribution dX, and xi are pairwise distinct real numbers.

TL;DR: The class of multivariate normal densities n (0, Σ ) whose inverse covariance matrix Σ −1 is an M-matrix is equivalent to this normal density being multivariate totally positive of order 2(MTP 2 ) as mentioned in this paper.

TL;DR: This paper presents two methods not requiring the explicit knowledge of the roots of r and obtains various properties of the similarity transformations between Jacobi matrices, which are proved by simple matrix calculus without using the generalized Christoffel theorem.

TL;DR: In this article, it was shown that such a B exists with m⩽ 1 2 k(k+1)−N, where 2N is the maximal number of entries which equal zero in a nonsingular principal submatrix of A.

TL;DR: In this article, it was shown that a matrix A admits a 1-inverse if and only if a linear combination of all the r × r minors of A is equal to one, where r is the rank of A.

TL;DR: In this paper, the sign matrices uniquely associated with the matrices (M − ζ j I ) 2, where the corners of a rectangle oriented at π /4 to the axes of a Cartesian coordinate system, were used to compute the number of eigenvalues of the arbitrarily chosen matrix M which lie within the rectangle, and to determine the left and right invariant subspaces of M associated with these eigen values.

TL;DR: In this paper, a complete description including multiplicity is given for the Jordan structure of a matrix which is a small perturbation of a known Jordan structure, and the problem solved here was solved independently and the other solution has been published in English.

TL;DR: In this article, the iterative aggregation method for the solution of a system of linear algebraic equations x = Ax + b, where A ≥ 0, b ≥ 0 and s > 0, and s < s, is proved to be locally convergent.

TL;DR: A robust Lanczos algorithm is presented which is fast, easy to understand, uses about 30 words of extra storage, and has a fairly short program.

TL;DR: In this paper, a new algorithm for the numerical calculation of the singular values and vectors of an infinite Hankel matrix of known finite rank r is presented, which proceeds by reduction to the singular value problem for an r × r matrix, achieved without solving for the poles of the symbol of H.

TL;DR: In this paper, a linear combination of n -by-n Hermitian matrices over the complex field was shown to be possible in a finite number of steps, where A and B are real symmetric sparse matrices.

TL;DR: In this article, the authors present an algorithm polvol for the computation of the d-dimensional volume V(P) of a bounded polyhedron P ⊂ R d, which is determined by the local properties of P at all its vertices.

TL;DR: In this article, the Euler-MacLaurin summation formula is used to deduce the Whittaker-Shannon sampling theorem for not necessarily band-limited functions, as well as to study numerical integration over the real axis.