Computation of Parameters in some Mathematical Models

In computational science it is normal to clarify dynamic systems by mathematical models in types of differential or integral equations. These models could have parameters which have to become computed for a model to get complete. For the special method of common differential equations studied with this dissertation, the resulting parameter estimation issue is a separable nonlinear least squares trouble with equal rights constraints. This trouble might be solved by iteration, but caused by complicated calculations of derivatives and also the information on several local minima, so called short-cut methods might be a substitute. These techniques depend on simplified versions in the original problem. A formula, named the modified Kaufman algorithm, is proposed also it takes the separability into consideration. Moreover, different varieties of discretizations and formulations of the optimization problem are discussed along with the effect of ill-conditioning Computation of parameters often includes as part solution of linear system of equations Ax = b. The related pseudoinverse solution relies on the properties of the matrix A and vector b. The singular value decomposition of the may then be utilized to construct error propagation matrices and also by using these it is easy to investigate how alterations in the input data impact the solution x. Theoretical error bounds based upon condition numbers indicate the even worst however the usage of experimental error analysis creates it achievable to even have more knowledge about the consequence of more limited degree of perturbations and in that sense become more realistic…

Contents: Computation of Parameters in some Mathematical Models

1 Why this kind of Research?
2 The Area of Research – Scientiﬁc Computing
2.1 Computational Science and Engineering
2.1.1 Computation of Model Parameters
2.2 Examples of Applications
2.3 Some Important Concepts
2.3.1 Dynamic Models and Differential Equations
2.3.2 Direct and Inverse Problems
2.3.3 Optimization and Linear Algebra
2.3.4 Computerizing and Approximations
2.3.5 Validation and Error Reduction
2.4 Historical Notes and Visions for the Future
2.5 Bibliography
3 Popul¨ arvetenskaplig sammanfattning p˚ a svenska
4 Summary of the Papers
4.1 Paper I & II
4.1.1 Contributions
4.1.2 Future Work
4.2 Paper III & IV
4.2.1 Contributions
4.2.2 Future Work