Tchebycheff approximation

Thesis (M.A.)--Boston Universit

Tchebycheff approximation on a discrete point set: algorithms old and new

Several linear and nonlinear algorithms for solving the discrete Tchebycheff problem are compared in this study. The Lawson algorithm is compared with two more well-known methods of linear Tchebycheff approximation. A new acceleration scheme for the Lawson algorithm is introduced and its performance is tested with an already existing acceleration technique. The new version is found to be better than the previous one but not as effective as the traditional Exchange method. A nonlinear version of Lawson\u27s algorithm is proposed for the solution of problems having approximating functions which are varisolvent. Some linear theorems of Lawson are extended to the nonlinear case. A modification of Osborne and Watson\u27s nonlinear method is introduced and tested on five problems. This new technique improves the efficiency remarkably, particularly for larger problems --Abstract, page ii

A two-stage probability based, conservatism reduction methodology for traditional Minimax robust control system design

A two-stage, probability-based controller design methodology is proposed to reduce the conservatism from traditional robust minimax controller design method, by relaxing the norm-bounded parameter uncertainty constraint and incorporating uncertain parameters' probabilistic information.Ph.D

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors

We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds.

Policy Evaluation in Uncertain Economic Environments

This paper develops a decision-theoretic approach to policy analysis. We argue that policy evaluation should be conducted on the basis of two factors: the policymaker's preferences, and the conditional distribution of the outcomes of interest given a policy and available information. From this perspective, the common practice of conditioning on a particular model is often inappropriate, since model uncertainty is an important element of policy evaluation. We advocate the use of model averaging to account for model uncertainty and show how it may be applied to policy evaluation exercises. We illustrate our approach with applications to monetary policy and to growth policy.

News, Noise, and Estimates of the "True" Unobserved State of the Economy

Which provides a better estimates of the growth rate of “true” U.S. output, gross domestic product (GDP) or gross domestic income (GDI)? Past work has assumed the idiosyncratic variation in each estimate is pure noise, taking greater variability to imply lower reliability. We develop models that relax this assumption, allowing the idiosyncratic variation in the estimates to be partly or pure news; then greater variability may imply higher information content and greater reliability. Based on evidence from revisions, we reject the pure noise assumption for GDI growth, and our results favor placing sizable weight on GDI growth because of its relatively large idiosyncratic variability. This calls into question the suitability of the pure noise assumption in other contexts, including dynamic factor models.