A systematic procedure is proposed for the design of multivariable feedback control systems. For an N x N multivariable control system, the desirable overall compensator is decomposed into N cascaded sub-compensators to be determined in each step. The stabilityequation method is used to find the desirable sub-compensators. After step N, the overall closed-loop system can be designed diagonal do...

We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlation coefficients. This representation holds for a large class of Gaussian g...

This note introduces an interesting class of Gauss-Markov Random Fields designated as walk-summable. Several equivalent characterizations of this class of GMRFs are established. Also, several important subclasses of GMRFs are identified as being walk-summable. These include (i) diagonally dominant, (ii) pairwise normalizable, (iii) regular singly-connected, and (iv) regular bipartite with only ...

Extended Abstract In this paper, we present a class of graph-based preconditioners for sparse linear systems arising from the finite element discretization of elliptic partial differential equations. A sparse matrix can be preconditioned by using a subgraph of its weighted adjacency matrix. The subgraph can be viewed as a " support graph " and the corresponding sparse matrix can be used as a pr...

Distance geometry is a branch of geometry which puts the concept of distance at its core. The fundamental problem of distance geometry asks to find a realization of a finite, but partially specified, metric space in a Euclidean space of given dimension. An associated problem asks the same question in a Euclidean space of any dimension. Both problems have many applications to science and enginee...

We consider algorithms for solving narrow-banded diagonally dominant linear systems which are suitable for multiprocessors. We describe a direct solver similar to that in [12] for tridiagonal systems, and in [9] for solving a banded system on a linearly connected set of processors. We will also provide and analyze a parallel implementation of the partitioning algorithm and the matrix decomposit...

Abstract Let C ( A ) = ∘ − T {\mathcal{C}}\left(A)=A\circ {A}^{-T} be the combined matrix of an invertible A , where \circ means Hadamard prod...

During recent decades, there have been a great number of research articles studying interior-point methods for solving problems in mathematical programming and constrained optimization. Stewart and O'Leary obtained an upper bound for scaled pseudoinverses sup W2P k(W 1 2 X) + W 1 2 k 2 of a matrix X where P is a set of diagonal positive deenite matrices. We improved their results to obtain the ...

The advantages of solving potential problems using an overdetermined boundary integral element method are examined. Representing a 2-dimensional potential solution by an analytic complex function forms two algebraic systems from the real and imaginary parts of the discretized form of the Cauchy theorem. Depending on which boundary condition is prescribed, the real or the imaginary algebraic sys...

We develop nearly-linear time algorithms for approximately solving sparse symmetric diagonally-dominant linear systems. In particular, we present a linear-system solver that, given an n-by-n symmetric diagonally-dominant matrix A with m non-zero entries and an n-vector b, produces a vector x̃ satisfying ‖x̃ − x‖A ≤ ǫ, where x is the solution to Ax = b, in time m log m+O (m log(1/ǫ)) + n2 √ log n ...