التفاصيل البيبلوغرافية
| العنوان: |
Gale duality, decoupling, parameter homotopies, and monodromy |
| المؤلفون: |
Niemerg, Matthew E., author, Bates, Daniel J., advisor, Shipman, Patrick, committee member, Peterson, Christopher, committee member, Lee, Chihoon, committee member |
| بيانات النشر: |
Colorado State University. Libraries |
| سنة النشر: |
2007 |
| المجموعة: |
Digital Collections of Colorado (Colorado State University) |
| مصطلحات موضوعية: |
gale duality, parameter homotopies, numerical algebraic geometry, monodromy |
| الوصف: |
2014 Spring. ; Numerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy. |
| نوع الوثيقة: |
text |
| وصف الملف: |
born digital; doctoral dissertations; application/pdf |
| اللغة: |
English |
| Relation: |
Niemerg_colostate_0053A_12232.pdf; http://hdl.handle.net/10217/82567 |
| الاتاحة: |
http://hdl.handle.net/10217/82567 |
| Rights: |
Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. |
| رقم الانضمام: |
edsbas.3F143D16 |
| قاعدة البيانات: |
BASE |