This paper gives sensitivity analyses by two approaches for L and U in the factor-ization A = LU for general perturbations in A which are suuciently small in norm. By the matrix-vector equation approach, we derive the condition numbers for the L and U factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting aaect th...

The noise sensitivity of interpolation and extrapolation matrices is investigated. For certain bandwidth and truncation parameters, the interpolation matrix is shown to yield results at a lower noise level than the input data. The input noise level, however, can be lowered by filtering the result. The noise level in the interpolated interval is shown to be lower near where the image is known. T...

— We use first-order perturbation theory to provide a local linear relation between the circuit parameters and the poles of an RLC network. The sensitivity matrix, which defines this relationship, is obtained from the systems eigenvectors and the derivative of its eigenvalues. In general, the sensitivity matrix is related to the equilibrium fluctuations of the system. In particular, it may be u...

matrix metalloproteinases (mmps) are a family of neutral proteinases that are important in normal development, cellular differentiation or migration, angiogenesis, neurogenesis, wound repair, and a wide range of pathological processes such as oxidative stress and neuroinflammation. mmps have been demonstrated to increase the permeability of the blood–brain barrier (bbb) by degrading the compone...

Introduction: MRI is increasingly used as a sensitive, noninvasive diagnostic modality for OA, but suffers from lack of specificity for matrix degradation. The initial phases of OA are characterized by disruption and loss of collagen and proteoglycan, the two major matrix components of cartilage. While changes in monoexponential relaxation times (e.g. T1, T2, and T1rho) have been observed to ac...

The abuse of market power is a potentially serious problem for market designers. Few if any indices exist to measure the potential for market power in real-time. In references [1-2] an expression for a dispatch-to-price sensitivity matrix, M, was derived. The expression requires information about network topology and parameters as well as the rules used to operate the market. While computing th...

A suitable design of state estimators requires a representative model for capturing the plant behavior and knowledge about the noise statistics, which are generally not known in practical applications. While the measurement noise covariance can be directly derived from the measurement device reproducibility, the choice of the process noise covariance is much less straightforward. Further, proce...

Nomenclature F = state transition matrix H = matrix giving the ideal/noiseless connection between measurements and states I = identity matrix k = time index L = noise sensitivity matrix in nonlinear systems N = lag time constant integer P = estimation-error covariance matrix s = arbitrary time step used in inductive proof xk = state at time index k x̂ = state estimate x̂k = a priori state estimat...