In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...

Efficient mode shape extraction of fluid-structure systems is of particular interest in engineering. An efficient modified version of unsymmetric Lanczos method is proposed in this paper. The original unsymmetric Lanczos method was applied to general form of unsymmetric matrices, while the proposed method is developed particularly for the fluid-structure matrices. The method provides us with si...

A well-known result of Lyapunov on continuous linear systems asserts that a real square matrix A is positive stable if and only if for some symmetric positive definite matrix X, AX + XA is also positive definite. A recent result of Moldovan-Gowda says that a Z-matrix A is positive stable if and only if for some symmetric strictly copositive matrix X, AX + XA is also strictly copositive. In this...

A one{to{one relation is established between the nonnegative spectral values of a vector in a primitive symmetric cone and the eigenvalues of its quadratic representation. This result is then exploited to derive similarity relations for vectors with respect to a general symmetric cone. For two positive deenite matrices X and Y , the square of the spectral geometric mean is similar to the matrix...

A STRUCTURED STAIRCASE ALGORITHM FOR SKEW-SYMMETRIC/SYMMETRIC PENCILS RALPH BYERS , VOLKER MEHRMANN , AND HONGGUO XU Abstract. We present structure preserving algorithms for the numerical computation of structured staircase forms of skew-symmetric/symmetric matrix pencils along with the Kronecker indices of the associated skew-symmetric/symmetric Kronecker-like canonical form. These methods all...

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a g...

Preconditioners are often conceived as approximate inverses. For nonsingular indeenite matrices of saddle-point (or KKT) form, we show how preconditioners incorporating an exact Schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues. Thus approximations of the Schur complement lead to preconditioners which can be very eeective even though they ar...

The minimum of quadratic functionals of the gradient on the set of convex functions ABSTRACT We study the innmum of functionals of the form R Mruru among all convex functions u 2 H 1 0 (() such that R jruj 2 = 1. (is a convex open subset of R N , and M is a given symmetric N N matrix.) We prove that this innmum is the smallest eigenvalue of M if is C 1. Otherwise the picture is more complicated...

Let X be a complex manifold, π:E→X locally trivial holomorphic fibration with fiber F, and (g,〈•,•〉) Lie algebra an invariant symmetric form. We associate to this data prefactorization Fg,π on in the formalism of Costello-Gwilliam. When X=C, g is simple, F smooth affine variety, we extract from vertex which vacuum module for universal central extension g⊗H0(F,O)[z,z−1]. As special case, when al...