LetX be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X , and let g denote the complexification of the Lie algebra of U , g = u. Each u-compatible triangular decomposition g = n − + h + n+ determines a Poisson Lie group structure πU on U . The Evens-Lu construction ([EL]) produces a (U, πU )-homoge...

In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of the chordal graph of ...

the sst decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. in this topic we are going to consider vectors as fuzzy vectors. we have considered a numerical example and tried to find out solution vector x in fuzzified form using method of sst decomposition.

A low-complexity multiple-input multiple-output (MIMO) subspace detection algorithm is proposed. It is based on decomposing a MIMO channel into multiple subsets of decoupled streams that can be detected separately. The new scheme employs triangular decomposition followed by elementary matrix operations to transform the channel into a generalized elementary matrix whose structure matches the sub...

We discuss algorithmic advances which have extended the pioneer work of Wu on triangular decompositions. We start with an overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory. We then present new techniques that we regard as essential to the recent success and for future research directions in the development of t...

Temporal and spatio-temporal data are present in many modern application systems, including monitoring moving objects. Such systems produce enormous volume of data, and therefore efficient indexing method is crucial. In this paper, we investigate and present a new concept based on virtual index structure, which can efficiently query such data. Concept is based on spatial representation of inter...

We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization PAP = LDL where P is a permutation matrix, L is lower triangular with a unit diagonal and D is symmetric block diagonal with 1×1 and 2×2 antidiagonal blocks. The novel algorithm requires O(n2rω−2) arithmetic o...