Author: S. van Huffel Publisher: Springer Science & Business Media ISBN: 9401735522 Category : Mathematics Languages : en Pages : 389
Book Description
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.
Author: Carl Friedrich Gauss Publisher: SIAM ISBN: 0898713471 Category : Mathematics Languages : en Pages : 240
Book Description
English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.
Author: Sabine Van Huffel Publisher: SIAM ISBN: 0898712750 Category : Mathematics Languages : en Pages : 302
Book Description
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.
Author: William Johnson Publisher: Createspace Independent Publishing Platform ISBN: 9781515101888 Category : Languages : en Pages : 0
Book Description
From the INTRODUCTORY. Errors of Observation. 1. A quantity of which the magnitude is to be determined is either directly measured, or, as in the more usual case, deduced by calculation from quantities which are directly measured. The result of a direct measurement is called an observation. Observations of the kind here considered are thus of the nature of readings upon some scale, generally attached to an instrument of observation. The least count of the instrument is the smallest difference recognized in the readings of the instrument, so that every observation is recorded as an integral multiple of the least count. 2. Repeated observations of the same quantity, even when made with the same instrument and apparently under the same circumstances, will nevertheless differ materially. An increase in the nicety of the observations, and the precision of the instrument, may decrease the discrepancies in actual magnitude; but at the same time, by diminishing the least count, their numerical measures will generally be increased; so that, with the most refined instruments, the discrepancies may amount to many times the least count. Thus every observation is subject to an error, the error being the difference between the observed value and the true value; an observed value which exceeds the true value is regarded as having a positive error, and one which falls short of it as having a negative error. 3. An error may be regarded as the algebraic sum of a number of elemental errors due to various causes. So far as these causes can be ascertained, their results are not errors at all, in the sense in which the term is here used, and are supposed to have been removed by means of proper corrections. Systematic errors are such as result from unknown causes affecting all the observations alike. These again are not the subjects of the "theory of errors," which is concerned solely with the accidental errors which produce the discrepancies between the observations.
Author: Ake Bjorck Publisher: SIAM ISBN: 9781611971484 Category : Mathematics Languages : en Pages : 425
Book Description
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Author: John Wolberg Publisher: Springer Science & Business Media ISBN: 3540317201 Category : Mathematics Languages : en Pages : 257
Book Description
Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods
Author: S. van Huffel
Author: William Woolsey Johnson
Author: Carl Friedrich Gauss
Author: Sabine Van Huffel
Author: William Johnson
Author: Ake Bjorck
Author: John Wolberg
Author: Thomas Wallace Wright
Author: 
Author: William Woolsey Johnson