Download or read book Convergence of Iterative Methods Applied to Large Overdetermined Linear and Nonlinear Systems of Equations Using Least Squares written by Charles O. Stearns and published by . This book was released on 1970 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions are obtained to large overdetermined systems of equations. Both nonlinear and linear systems are considered. The nonlinear system represents a dipole model of the earth's geomagnetic field, which is generated from spherical harmonic coefficients. This system of 64 unknowns and 1836 equations is solved by a maximum neighborhood method, which is an optimum interpolation between the well known Taylor's series and steepest descent methods. The original given values of the generated field are as large as 60,000 gamma, whereas a rms residual of 27.9 gamma is obtained with 173 iterations. The linear system of equations represents dipole changes required to account for the earth's secular change field which is generated from spherical harmonic coefficients. The dipole parameters computed from the nonlinear model are used as input parameters. The system contains 64 unknowns and 612 equations and is solved using a Chebyshev polynomial iterative method. These results are compared to results obtained by a direct solution of the normal equations of the system and results obtained by a pseudo-inverse method using a modified Gram-Schmidt factorization. Although the latter two methods give smaller rms values than the iterative method, the results of the iterative method are more reasonable in view of known properties of the results. The generated field has a rms value of 45 gamma per year. An rms residual of 2.5 gamma per year was obtained after 25,000 iterations.

Download or read book Monthly Catalogue United States Public Documents written by and published by . This book was released on 1970 with total page 1730 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1981 with total page 1370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book ESSA Technical Report ERL ESL written by and published by . This book was released on 1967 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ESSA Technical Report ERL written by United States. Environmental Science Services Administration and published by . This book was released on 1970 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Research in Progress written by and published by . This book was released on 1978 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monthly Catalog of United States Government Publications written by United States. Superintendent of Documents and published by . This book was released on 1966 with total page 1320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monthly Catalog of United States Government Publications Cumulative Index written by United States. Superintendent of Documents and published by . This book was released on 1970 with total page 1348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-12-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.

Download or read book Boundary Elements and Other Mesh Reduction Methods XXXII written by C. A. Brebbia and published by WIT Press. This book was released on 2010 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the 32nd International Conference on Boundary Elements and Other Mesh Reduction Methods, an internationally recognized forum for the dissemination of the latest advances on mesh reduction techniques and their applications in science and engineering.

Download or read book A Matrix Algebra Approach to Artificial Intelligence written by Xian-Da Zhang and published by Springer Nature. This book was released on 2020-05-23 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.

Download or read book Petroleum Abstracts written by and published by . This book was released on 1970 with total page 1394 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book NOAA Technical Report ERL written by and published by . This book was released on 1972 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Commerce Today written by and published by . This book was released on 1970 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ESL written by and published by . This book was released on 1972 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt: