Some `Golden Oldie' Technical Reports and Papers
of Grace Wahba
Grace Wahba unpublished old technical reports
and selected earlier papers
that have some modern day relevance
are scanned in here (mostly pdf).
1. Unpublished Technical Reports:
1986
- Wahba, G.
"
GCVPACK-Routines for Generalized Cross Validation
" TR 775(rev), D. Bates, M. Lindstrom, G. Wahba
and B. Yandell. May 1987. Documentation
for GCVPACK. Code available via
netlib.
An earlier version has appeared in Commun. Statist. Simul. Comput.,
1987, v 16, pp263-297.
1980
1978
1969
- Wahba, G.
"
Estimating derivatives from outer space
" Mathematics Research Center
TSR 989, May 1969. This paper solves a
variational problem of the form: find $f$ to minimize
a semi-norm in a reproducing kernel Hilbert space
subject to the condition that the values of $f$ at
specified points are within specified intervals.
Can be viewed as a precursor to what is called "Support Vector Regression".
1967
2. Selected Earlier Papers:
1993
1992
1991
- Wahba, G., Johnson, D. R, and Reames, F.
"
Multiple smoothing and weighting parameters in
direct variational methods for objective analysis
of meteorological information
"
In "Assimilation of Observations in Meteorology and
Oceanography", Proceedings of the WMO International
Symposium, Clermont-Ferrand, 1990,
F.- X. LeDimet and O. Talagrand, eds., WMO, 448-453 (1991).
1990
1989
1988
1987
- Wahba, G.
"
Three topics in Ill-posed Problems.
" This paper has appeared in "Inverse and
Ill-Posed Problems, M. Engl and G. Groetsch, Eds.,
Academic Press 1987, pp 37-50. Among other things provides a discussion
of how early stopping of iterative methods for solving large
linear systems is a form of regularization.
1986
1985
1984
1983
1982
- Wahba, G.
"
Vector Splines on the Sphere, With Application to the
Estimation of Vorticity and Divergence from Discrete,
Noisy Data
" These vector splines may be used
to estimate wind fields, and also to
fit smooth transformations of the sphere
onto itself, of possible application to the fitting
of non-isotropic covariances. In 'Multivariate Approximation
Theory II, W. Schempp and K. Zeller, eds. Birkhauser Verlag
1982.
[This paper was
scanned and then `Capture' was used to translate
the scanned pdf into letters. It does not do equations,
and occasionally it could not interpret a word. In that
case the original scanned word is retained, and it looks
funny. Please ignore.]
- Wahba, G.
"
Variational Methods in Simultaneous Optimum Interpolation
and Initialization
" This paper has appeared in
`The Interaction Between Objective Analysis and
Initialization', Proceedings of the Fourteenth
Stanstead Seminar, 1982. D. Williamson, Editor.
It is primarily of historical interest, since the
results are by now widely understood.
It may be one of the earliest papers in the meteorological
literature to relate the
relationshop between variational methods and Bayes estimates.
1981
- Wahba, G.
"
Numerical experiments with the thin plate histospline
" This paper has appeared in
Commun. Statist. Theor. Meth., A10(24),
2475-2514 (1981). It has application to the
problem of fitting models for data that
has been aggregated over irregular geographical
regions such as counties or states.
You will need acrobat to read it.
- Wahba, G.
"
Spline Interpolation and Smoothing on the Sphere
" This paper has appeared in
SIAM J. Sci. Stat. Comput, (2),
5-16(1981) and an important errata sheet [(3),385-6,(1982)] is
attached at the end of the scanned pdf file.
The splines on the sphere have power law
decay in their energy distributions.
1980
1979
1978
1977
- Wahba, G.
"
Practical Approximate Solutions to Linear Operator Equations When the
Data Are Noisy
",
SIAM J. Numer. Anal.,
14, 4 (1977) 651-667. This very early paper describes the key
role of reproducing kernels in the regularized
solution of ill-posed inverse problems.
What amounts to the GCV estimate of the smoothing parameter lambda is
discussed (but called
"weighted cross validation" there), and various convergence rates
when using this lambda are given. It is shown how the
rates are related to the rate of decay of the eigenvalues of the reproducing kernel.
1974
1973
1971
- Kimeldorf, G. and Wahba, G.
"
Some results on Tchebycheffian Spline
Functions ",
J. Mathematical Analysis and Applications,
33, 1 (1971) 82-95. This paper describes the form of
the solution of a class of variational problems in
RKHS when the observables are related to bounded linear
functionals in the space (including evaluation functionals)!
[The proof of the "representer theorem".]
A connection with Bayes estimates and variational problems
in RKHS is also noted.
1970
1969
1968
1966
- Wahba, G.
"
A Least Squares Estimate of Satellite Attitude
",
SIAM Review,
8, 3, (1966) 384-386. This problem, with solution, was proposed
to the SIAM Review by G. Wahba. In keeping with their custom,
several solutions other than that by the proposer were printed,
beginning with one by Farrell and Stuelpnagel. It is known
in the aeronautics literature as "Wahba's Problem".