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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.
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.
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
An overview of the computational issues; statistical, numerical, and algebraic properties, and new generalizations and applications of advances on TLS and EIV models. Experts from several disciplines prepared overview papers which were presented at the conference and are included in this book.
Mastronardi, Lemmerling, and van Huffel presented an algorithm for solving a total least squares problem when the matrix and its perturbations are Toeplitz. A Toeplitz matrix is a special kind of matrix with small displacement rank. Here we generalize the fast algorithm to any matrix with small displacement rank. In particular, we show how to efficiently construct the generators whenever M has small displacement rank and show that in many important cases the Cholesky factorization of the matrix MT̂M can also be determined fast. We further extend this problem to Tikhonov regularization of ill-posed problems and illustrate the use of the algorithm on an image deblurring problem.
raster. Generalizations of the lattice filter and spectral factorization problems to the polar raster are also addressed.