On September 17, 1939 the Soviet Union invaded Poland from the east per an
agreement with Germany. Poland was effectively dissolved as a nation by the first
week of October. In the course of the invasion Soviet troops took well over two
hundred thousand Polish soldiers and civilians prisoner (perhaps even three times
that number) . Until the Germans invaded eastern Poland during Operation
Barbarossa in June 1941 the Soviet Union was engaged in wholesale deportation and
slaughter of prisoners. There are no reliable figures on deportations from Poland to
Germany or Russia - perhaps as few as 350,000 to as many as 1,625,000. Similarly, the
approximate number of prisoners killed by the Soviets during the first occupation
varies considerably from 20,000 to 40,000 or more.
There were very few bright moments even in the United States: in 1944 Roosevelt assigned his special
emissary to the Balkans, Navy Lieutenant Commander (and Governor of Pennsylvania 1937-9 and US
Ambassador to Austria 1933-4) George Howard Earle, to investigate Katyn. Roosevelt rejected the
conclusion that the Soviet Union was responsible, declared that he was convinced Nazi Germany was to
blame and ordered the report suppressed. When Earle formally requested permission to publish his
findings, the President issued a written order to desist and reassigned Earle to American Samoa.
Most prisoners at Kozielsk, Starobielsk, Ostashkov, several smaller camps and a collection of
Belarusian and Ukrainian prisons were killed by gunshot and buried in mass graves during March and
April of 1940. Known nationalities include Polish, Russian, Ukrainian, Latvian, Lithuanian, Muslim
Tatar, Jewish, Georgian, and Belarusian. Besides soldiers there were university professors, physicians,
lawyers, engineers, teachers, writers, clergy, journalists and pilots. The NKVD executed about half of
all Polish military officers.
Among the professors killed was Stefan Kaczmarz who was born in 1895 in Lviv (also known as
Lemberg) in the province of Galicia, then part of Austria-Hungary and now part of the Ukraine. Part of
his mathematical work involved the rapid solution of systems of linear equations. One might say his
name still radiates because among the applications today are the famed CAT scan as well as a number
of optical and acoustic uses. What was needed was given large sets of observations such as tomography
slices to reconstruct the configuration of the original object.
Recent work in the area includes
Herman, G. T., Fundamentals of computerized tomography: Image reconstruction from projection,
2nd edition, Springer, 2009.
Censor, Y. and S.A. Zenios, Parallel optimization: theory, algorithms, and applications. Oxford
University Press, New York. 1997.
Strohmer, T., and R. Vershynin, A randomized Kaczmarz algorithm for linear systems with exponential
convergence, Journal of Fourier Analysis and Applications, vol. 15, pp. 262-278, 2009.
Censor, Y., G. T. Herman, and M. Jiang, A note on the behavior of the randomized Kaczmarz algorithm
of Strohmer and Vershynin, Journal of Fourier Analysis and Applications. vol. 15, pp. 431-436, 2009.
A Master's Thesis in Molecular Physiology and Biophysics at Vanderbilt by Latsavongsakda
Sethaphong in 2008.
We are currently using Kaczmarz techniques to attempt to make sense of seismic event aftershocks,
which are, after all, just another instance of waves reflecting from an object.