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Fast algorithms for solving large-scale structural optimization and least squares problems are being investigated. An especially significant aspect of this work is the development and testing of parallel algorithms for alternatives to the often ill-conditioned stiffness equations approach in structural analysis on machines such as the Cray X-MP, the Denelcor HEP and the Intel Hypercube. The principal thrusts in this project on least squares methods have been in developing techniques for the solution of superlarge problems in a stable way, i.e., employing orthogonal factorization techniques, on multiprocessors. These computations involve various levels of parallelism, including domain decomposition as well as pipelining type schemes for orthogonal factorization. Additional keywords: linear algebra; parallel processing. (Author).
This report summarizes the activities in support of the Air Force Research Project AFOSR-83-0255 during the past year. Efforts have been made to develop, test and analyze new fast techniques in matrix analysis for structural computations and least squares problems. Applications of this work include structural design and dynamics, and least squares filtering in signal processing. Implementations and tests have been made on modern high performance architectures such as the Cray X-MP, Alliant FX/8, Sequent Balance and the Intel iPSC Hypercube. Our recent work on parallel algorithms for near real-time signal processing computations has led to especially significant results. Keywords: Abstracts; Numerical linear; Algebra; Parallel processing; Signal processing, Structural optimization. (Author).
New fast algorithms for high speed computation on the modern generation of supercomputers is essential. To meet these challenges new techniques are developed in numerical linear algebra and its applications for implementation on these new architectures. Significantly, applications of this work to practical problems of structural analysis and design and to least squares adjustments, estimation and digital filtering are also being investigated. The current objectives in structural analysis are to develop efficient and stable high speed algorithms for the design and analysis of large complex systems. Interest here is in developing stable alternatives to the often ill conditioned stiffness matrix approach to solving problems in elastic analysis and structural dynamics. For example, a comparative study is developed of the performances of seven alternative methods to the stiffness approach on the Alliant FX/8 and Cray X-MP systems. These methods involve various orthogonal factorization approaches as well as preconditioned conjugate gradient methods which completely avoid formation of the stiffness equations.
Fast algorithms for solving numerical problems involving large sparse matrix computations are investigated. Applications of this work to the areas of structural analysis, constrained optimization and large scale least squares adjustment methods are developed. One of the more important accomplishments is the design and testing on the Denelcor HEP multiprocessor of a parallel algorithm for computing a banded basis matrix for the null space. This algorithm may lead to a new efficient sparse matrix implementation of the force method for the finite element analysis of large-scale structures.
Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.
raster. Generalizations of the lattice filter and spectral factorization problems to the polar raster are also addressed.
Basics of Computational Geophysics provides a one-stop, collective resource for practitioners on the different techniques and models in geoscience, their practical applications, and case studies. The reference provides the modeling theory in an easy-to-read format that is verified with onsite models for specific regions and scenarios, including the use of big data and artificial intelligence. This book offers a platform whereby readers will learn theory, practical applications, and the comparison of real-world problems surrounding geomechanics, modeling and optimizations. Covers various advanced computational techniques for solving different problems in geophysics, including the use of Big Data and artificial intelligence Includes case studies that provide examples surrounding practical applications Provides an assessment of the capabilities of commercial software