Journal ArticleDOI
Solution of the matrix equation AX + XB = C [F4]
R. H. Bartels,G. W. Stewart +1 more
Reads0
Chats0
TLDR
The algorithm is supplied as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape, and the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 (U.S.and Canada) or $18.00 (elsewhere).Abstract:
and Canada) or $18.00 (elsewhere). If the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 (U.S. only). All orders are to be prepaid with checks payable to ACM Algorithms. The algorithm is re corded as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape. We will supply the algorithm at a density of 800 B.P.I. if requested. The cards for the algorithm are sequenced starting at 10 and incremented by 10. The sequence number is right justified in colums 80. Although we will make every attempt to insure that the algorithm conforms to the description printed here, we cannot guarantee it, nor can we guarantee that the algorithm is correct.-L.D.F. Descdption The following programs are a collection of Fortran IV sub-routines to solve the matrix equation AX-.}-XB = C (1) where A, B, and C are real matrices of dimensions m X m, n X n, and m X n, respectively. Additional subroutines permit the efficient solution of the equation ArX + xa = C, (2) where C is symmetric. Equation (1) has applications to the direct solution of discrete Poisson equations [2]. It is well known that (1) has a unique solution if and only if the One proof of the result amounts to constructing the solution from complete systems of eigenvalues and eigenvectors of A and B, when they exist. This technique has been proposed as a computational method (e.g. see [1 ]); however, it is unstable when the eigensystem is ill conditioned. The method proposed here is based on the Schur reduction to triangular form by orthogonal similarity transformations. Equation (1) is solved as follows. The matrix A is reduced to lower real Schur form A' by an orthogonal similarity transformation U; that is A is reduced to the real, block lower triangular form.read more
Citations
More filters
Passive Control of Linear Systems
TL;DR: This work proposes a method for designing optimal damping viscosities of dampers in order to calm down vibrations of a structure with given mass and stiffness parameters based on the minimization of the trace of the Lyapunov equation in the underlying phase space equipped with the energy norm.
Journal ArticleDOI
Smoothness Regularized Multiview Subspace Clustering With Kernel Learning
TL;DR: To capture the nonlinear relations between multiview data points, the proposed model maps the concatenatedMultiview observations into a high-dimensional kernel space, in which the linear relations reflect the non linear relations between multi-view data points in the original space.
A Sylvester-Arnoldi type method for the generalized eigenvalue problem with two-by-two operator determinants
Karl Meerbergen,Bor Plestenjak +1 more
TL;DR: In this paper, a generalized eigenvalue problem of the form (B1 ⊗A2 −A1⊗B2)z = μ(B1 ∈ C2 − C1 ⌈ B2 )z is solved by solving a Sylvester equation with shift-and-invert transformation.
Journal ArticleDOI
Analysis and optimization of multiple tuned mass dampers with coulomb dry friction
Sung-Yong Kim,Cheol-Ho Lee +1 more
TL;DR: In this paper, the Coulomb dry friction force is incorporated as an energy dissipation mechanism to deal with the nonlinearity of the CDF force, which is a source of difficulty in the optimization process, and a statistical linearization that replaces the original nonlinear system with an equivalent linear system is adopted.
Proceedings ArticleDOI
LUDIA: an aggregate-constrained low-rank reconstruction algorithm to leverage publicly released health data
Yubin Park,Joydeep Ghosh +1 more
TL;DR: This paper introduces LUDIA, a novel low-rank approximation algorithm that utilizes aggregation constraints in addition to auxiliary information in order to estimate or "reconstruct" the original individual-level values from aggregate data.
References
More filters
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
The Direct Solution of the Discrete Poisson Equation on a Rectangle
TL;DR: In this article, the authors provide a survey of direct methods for solving finite difference equations with rectilinear domains. But the authors do not discuss whether the methods are easily adaptable to more general regions, and to general elliptic partial differential equations.
Journal ArticleDOI
TheQ R algorithm for real hessenberg matrices
TL;DR: The volume of work involved in a QR step is far less if the matrix is of Hessenberg form, and since there are several stable ways of reducing a general matrix to this form, the QR algorithm is invariably used after such a reduction.
Journal ArticleDOI
Matrix and other direct methods for the solution of systems of linear difference equations
W. G. Bickley,J. McNamee +1 more
TL;DR: In this paper, the problem of boundary problems arising in the approximate solutions of linear PDEs was investigated. But the work was conducted on desk machines, and the operations involved are, however, capable of being handled efficiently and simply by modern high-speed digital computers.