Iterative Refinement Scheme Research Articles

Adaptive Iterative Refinement of an Optimal 2DF Nonlinear Controller

The paper extends the generic two-degree of freedom controller scheme introduced for linear plants to factorable nonlinear processes. The simple cases of the Hammerstein and Wiener type block-oriented nonlinear models are analyzed and an iterative controller refinement scheme is presented. Simulation examples are also given to present the efficiency of the new methodology.

Using the Matrix Sign Function to Compute Invariant Subspaces

The matrix sign function has several applications in system theory and matrix computations. However, the numerical behavior of the matrix sign function, and its associated divide-and-conquer algorithm for computing invariant subspaces, are still not completely understood. In this paper, we present a new perturbation theory for the matrix sign function, the conditioning of its computation, the numerical stability of the divide-and-conquer algorithm, and iterative refinement schemes. Numerical examples are also presented. An extension of the matrix-sign-function-based algorithm to compute left and right deflating subspaces for a regular pair of matrices is also described.

An Iterative Redesign Technique of Reference Models: How to Reach the Maximal Bandwidth?

Abstract A generic optimal controller structure and regulator design method for linear systems are combined to form an iterative regulator refinement scheme, where the identification and control errors are identical. It is shown how a real nonlinear actuator limiting the amplitude of the control signal influences the control performances. Then the special modification of the original iterative scheme is presented, which allows the user to find the reachable maximal bandwidth by an iterative redesigning the original not reachable requirements. The effectiveness and usability of this new method is demonstrated by simulation examples.

Accuracy and effectiveness of preconditioned conjugate gradient algorithms for large and ill-conditioned problems

Different implementations of the preconditioned conjugate gradient method are presented for solving large and very ill-conditioned algebraic systems of equations resulting from the finite element method. A special implementation based on mixed precision calculations proved to be robust in performance and reliable in accuracy as well as storage effective. Additionally, a new type of iterative refinement scheme is introduced to improve the accuracy of direct methods based on conjugate gradient iterations; it is found to be a significant improvement on the standard iterative refinement approach.

A note on iterative refinement schemes for Sylvester operator equations

We propose two iterative schemes to refine an approximate solution of a Sylvester operator equation Kx − xθ = y , where K is a bounded linear operator in a Banach space B, K its extension to the product space X = B m , and θ ∈ C m× m . An approximate solution x n is obtained by means of an approximation K n to K. Then, x n is refined by two iterative processes involving the resolution, for e n , of K n e n − e nθ = r n , with different second members r n . In these processes, K is only used for evaluations.

On the Stability of Singular Finite-Rank Methods

The solution of the operator equation $(\lambda - {\bf \mathcal{K}})x = y$, where ${\bf \mathcal{K}}$ is a bounded linear operator of finite rank on a Banach space X and $\lambda $ is a nonzero scalar, can be reduced to the solution of a system of linear equations $(\lambda - {\bf \tilde{\mathcal{K}}} \mathcal{K})\alpha = \beta $, where ${\bf \tilde{\mathcal{K}}}$ is a matrix. A recent result of Whitley for the case where $\lambda $ is in the resolvent set of ${\bf \mathcal{K}}$ is extended to include the case where $\lambda $ is a nonzero spectral value of ${\bf \mathcal{K}}$. If $\lambda $ is a nonzero semisimple eigenvalue of ${\bf \mathcal{K}}$, then the stability of a particular solution of the linear system is related to the stability of a particular solution of the operator equation. Bounds for the condition number of an equivalent nonsingular linear system are given. These results are applied to the implementation of some iterative refinement schemes for approximating a nonzero simple eigenvalue o...

A stable geotomography technique for refractive media

The application of tomographical techniques to geophysical monitoring and exploration has been extended to media where refraction and reflection effects may be significant. The result is an iterative refinement scheme which is unstable in its original formulation. This paper presents the stability improvements of selective smoothing and path elimination which enable the reconstruction process to converge to an accurate solution. By use of the objective error measures of Euclidean distance and boundary definition by minimum variance partitioning, tomograms produced by this improved technique are shown to be superior to those obtained by traditional straight-line geotomography. Guidelines for practical application are presented.

A numerical inversion scheme for geoelectrical soundings

A simple numerical inversion scheme for estimatingn-layer model parameters from observed geoelectrical resistivity data can be used in either the space or wavenumber domain. The technique utilizes Madden's Transmission Line Analogy to compute the resistivity transforms and linear filter theory to accomplish the excursions between the space and wavenumber domains. The inversion is effected by an iterative refinement scheme employing the stochastic inverse which is approximate to the generalized inverse. No singular decomposition analysis is required and the scheme is stable under ill conditions. The inversion scheme not only gives the desired estimates; it exposes redundant parameters and irrelevant data and is easily programmed on a desk-top mini computer. Examples of inverse modeling with hypothetical and field data are discussed.