The feedback synthesis of linear systems satisfying certain exponential bounds on their transient behavior is studied. We present sufficient conditions ensuring that there exists a state feedback matrix such that the closed loop system satisfies a desired exponential growth bound. Special interest is directed to the case of generating contraction semigroups, which under certain conditions can b...

We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of observation impact matrix. We illustrate the application of this methodology to important a...

An equation adjoint to the luminance equation for describing the global illumination can be formulated using the notion of a surface potential to illuminate the region of interest This adjoint equation which we shall call as the potential equation is fundamental to the adjoint radiosity equation used to devise the importance driven radiosity algorithm In this paper we rst brie y derive the adjo...

The aim of this study is to introduce an innovative concept T-spherical fuzzy matrix, which a hybrid structure matrix and set. This article introduces the square constant discusses related properties. Determinant adjoint are also established, some properties investigated. An application in decision-making problem with illustrative example discussed here. Then, end, check capability viability, p...

on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...

Let k be an integral domain, n a positive integer, X a generic n×n matrix over k (i.e., the matrix (xij) over a polynomial ring k[xij ] in n 2 indeterminates xij), and adj(X) its classical adjoint. For char k = 0 it is shown that if n is odd, adj(X) is not the product of two noninvertible n×n matrices over k[xij ], while for n even, only one particular sort of factorization can occur. Whether t...

In a previous paper we proposed a preconditioning technique that generalizes an idea by M. Griebel. In this generalization, although all considerations are presented in a very general algebraic framework, the main idea behind them is to use as preconditioner a rectangular matrix constructed with the transfer operators between successive discretization levels of the initial problem. In this way ...