## Least Squares Data Fitting## with ApplicationsPer Christian Hansen, Victor Pereyra, and Godela Scherer
Johns Hopkins University Press, 2012 This site contains material related to the above book. |

- Page x (Preface), line 10: "P.-. Wedin" should be "P.-Å. Wedin".
- Page 6, Eq. (1.2.6): the
*x*below "min" should be boldface, twice. - Page 27, Eq. (2.1.1): the
*x*below "min" should be boldface. - Page 40, Theorem 26: the
*x*and*y*below "min" should be boldface, and*b*in the theorem's first displayed equation should be boldface. - Page 44, line 7: the
*x*below "min" should be boldface. - Page 88, line 10: the
*x*below "min" should be boldface. - Page 101, first displayed eq.: the
*y*below "min" should be bolface. - Page 109, line 17: the
*x*in Φ(*x*) should be boldface. - Page 115, displayed eq. on the middle of the page: the
*x*below "min" should be boldface, and so should the one in*x*^{(k)}. - Page 166, Eq. (9.2.2): the subscript to "min" should be
Δ
*x*(not Δ_{k}*x*_{k}_{+1}). - Page 170, the displayed equation above (9.3.1): same as above.
Also, the last term should be
|| Δ
*x*||_{k}_{2}^{2}(not ||*x*||_{k}_{2}^{2}). - Page 172, line 4 (the displayed equation for ρ
): change the sign of the denominator._{k} - Page 172, second bullet in the parameter updating algorith: the last
equation should read λ
_{k+1}= 2 λ_{k}. - Page 180, Eq. (9.5.5): the sign should be + instead of − in the Newton update.
- Page 188, Eq. (9.7.2): change
*x = x*to_{i}^{*}*x*._{i}= x_{i}^{*} - Page 213, line -4: change 11.2.1 to 11.2.2.

- Linear data fitting, covering Sections 1.1, 1.2, 1.4, 2.1, and 2.2.
- Nonlinar data fitting, covering Sections 8.1, 8.2, 9.1, 9.2, and 9.3.

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Scientific computing is founded in models that capture the properties
of systems under investigation, be they engineering systems; systems
in natural sciences; financial, economic, and social systems; or
conceptual systems such as those that arise in machine learning or
speech processing. For models to be useful, they must be calibrated
against "real-world" systems and informed by data. The recent
explosion in availability of data opens up unprecendented
opportunities to increase the fidelity, resolution, and power of
models - but only if we have access to algorithms for incorporating
this data into models, effectively and efficiently.
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For this reason, least squares - the first and best-known technique
for fitting models to data - remains central to scientific
computing. This problem class remains a fascinating topic of study
from a variety of perspectives. Least-squares formulations can be
derived from statistical principles, as maximum-likelihood estimates
of models in which the model-data discrepancies are assumed to arise
from Gaussian white noise. In scientific computing, they provide the
vital link between model and data, the final ingredient in a model
that brings the other elements together. In their linear variants,
least-squares problems were a foundational problem in numerical linear
algebra, as this field grew rapidly in the 1960s and 1970s. From the
perspective of optimization, nonlinear least-squares has appealing
structure that can be exploited with great effectiveness in algorithm
design.
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Least squares is foundational in another respect: It can be extended
in a variety of ways: to alternative loss functions that are more
robust to outliers in the observations, to one-sided "hinge loss"
functions, to regularized models that impose structure on the model
parameters in addition to fitting the data, and to "total least
squares" models in which errors appear in the model coefficients as
well as the observations.
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This book surveys least-squares problems from all these
perspectives. It is both a comprehensive introduction to the subject
and a valuable resource to those already well versed in the area. It
covers statistical motivations along with thorough treatments of
direct and iterative methods for linear least squares and optimization
methods for nonlinear least squares. The later chapters contain
compelling case studies of both linear and nonlinear models, with
discussions of model validation as well as model construction and
interpretation. It conveys both the rich history of the subject and
its ongoing importance, and reflects the many contributions that the
authors have made to all aspects of the subject.
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