Now showing items 1-10 of 22
Detecting Periodic Components in a White Gaussian Time Series
A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to the trimmed mean of the periodograms. The ...
SIMEST: An Algorithm for Simulation Based Estimation of Parameters Characterizing a Stochastic Process
The axioms defining stochastic processes are generally simple. However, estimation of the parameters of a process from data is extremely difficult if customary techniques are used. This is due to the complexities involved ...
Domain Decomposition for Two-Dimensional Elliptic Operators on Vector and Parallel Machines
The efficient computation of the solution to self-adjoint elliptic operators is the subject of this dissertation. Discretization of this equation by finite differences or finite elements yields a large, sparse, symmetric ...
Weighted Least Squares Estimators on the Frequency Domain for the Parameters of a Time Series
A procedure for estimating the parameters of a time series is proposed. The estimate minimizes a criterion function which is the weighted sum of squares of the distances between the periodograms and the spectrum of the ...
Electromagnetic Propagation and Scattering in Spherically-Symmetric Terrestrial System-Models
A study of the quantitative solutional approaches to boundary-value problems associated with terrestrial electromagnetic propagation is carried out, with particular attention given to spherical-system models and the frequency ...
A Multi-Level Domain Decomposition Algorithm Suitable for the Solution of Three-Dimensional Elliptic Partial Differential Equations
A three-dimensional, nonsymmetric, domain decomposition algorithm is developed. The algorithm is based upon the use of a lower dimensional problem as a correction to the preconditioned generalized conjugate residual method ...
A Stochastic Model Providing a Rationale for Adjuvant Chemotherapy
A model yielding the probability of curative outcome for a patient at the time of tumor detection is presented. The status of the patient is determined by whether or not metastases (distant spread of the tumor) have occurred ...
Algorithms for Solving Sparse Nonlinear Systems of Equations
In this thesis, we present four algorithms for solving sparse nonlinear systems of equations: the partitioned secant algorithm, the CM-successive displacement algorithm, the modified CM-successive displacement algorithm and the combined secant algorithm. The partitioned secant algorithm is a combination of a finite difference algorithm and a secant algorithm which requires one less function evaluation at each iteration than Curtis, Powell and Reid's algorithm (the CPR algorithm). The combined secant algorithm is a combination of the partitioned secant algorithm and Schubert's algorithm which incorporates the advantages of both algorithms by considering some special structure of the Jacobians to further reduce the number of function evaluations. The CM-successive displacement algorithm is based on Coleman and Moré's partitioning algorithm and a column update algorithm, and it needs only two function values at each iteration. The modified CM-successive displacement algorithm is a combination of the CM-successive displacement algorithm and Schubert's algorithm. It also needs only two function values at each iteration but it uses the information at every step more effectively. The locally q-superlinear convergence results, the r-convergence order estimates and the Kantorovich-type analyses show that these four algorithms have good local convergence properties. The numerical results indicate that the partitioned secant algorithm and the modified CM-successive displacement algorithm are probably more efficient than the CPR algorithm and Schubert's algorithm....
A Note on Detecting Simple Redundancies in Linear Systems
Two efficient algorithms are presented that, for a given linear system Ax=b, eliminate equations that are nonzero multiples of other equations. The second algorithm runs in linear time when the entries of A are +1, -1, or 0.
A Variable Metric Variant of the Karmarkar Algorithm for Linear Programming
The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration. We present a variant of the Karmarkar algorithm ...