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Now showing items 1-10 of 22

#### Electromagnetic Propagation and Scattering in Spherically-Symmetric Terrestrial System-Models

(1986-04)

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 ...

#### Linear and Nonlinear Deconvolution Models

(1986-04)

This dissertation considers computational methods for solving linear and nonlinear least squares problems arising from deconvolution applications. For the linear problems we propose a new preconditioner to speed up the ...

#### Algorithms for Solving Sparse Nonlinear Systems of Equations

(1986-04)

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 Multi-Level Domain Decomposition Algorithm Suitable for the Solution of Three-Dimensional Elliptic Partial Differential Equations

(1986-04)

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 ...

#### Conjugate Residual Methods for Almost Symmetric Linear Systems

(1986-04)

This study concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising from seismic inverse problems. We focus on an application which has two distinguishing features. The first ...

#### Histogram Estimators of Bivariate Densities

(1986-04)

One-dimensional fixed-interval histogram estimators of univariate probability density functions are less efficient than the analogous variable-interval estimators which are constructed from intervals whose lengths are ...

#### A Variable Metric Variant of the Karmarkar Algorithm for Linear Programming

(1986-06)

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 ...

#### Successive Column Correction Algorithms for Solving Sparse Nonlinear Systems of Equations

(1986-05)

This paper presents two algorithms for solving sparse nonlinear systems of equations: the CM-successive column correction algorithm and the modified CM-successive column correction algorithm. A q-superlinear convergence ...

#### The Combined Schubert/Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations

(1986-05)

This paper presents an algorithm, the combined Schubert/secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is based on dividing the columns of the Jacobian into two parts, ...

#### Multi-Model Algorithms for Optimization

(1986-04)

A recent approach for the construction of nonlinear optimization software has been to allow an algorithm to choose between two possible models to the objective function at each iteration. The model switching algorithm ...