Charles W. Groetsch,
Citadel Distinguished Professor of Mathematical Science
Office: (843) 953-5036 fax: (843) 953-7391
e-mail:
Vitae updated November, 2011
EDUCATION
B.S., M.S., University of New Orleans; Ph.D. Louisiana State University
EXPERIENCE
Associate Engineer, Applied Mathematics Department, Space Division, Launch Systems Branch, Boeing Company, 1966-68
Visiting Assistant Professor of Mathematics, University of Rhode Island, 1974-75
Assistant Professor, University of Cincinnati, 1971-75
Consultant, Management Decisions Development Corp., Cincinnati, 1976-82
Director of Graduate Studies, Mathematics Dept., Univ. of Cincinnati, 1975-79
Associate Professor, University of Cincinnati, 1976-81
Research Associate, USAF Flight Dynamics Laboratory, Summer, 1978
Senior Visiting Fellow, University of Manchester, England, Summer and Fall,1980
Professor of Mathematics, University of Cincinnati, 1981-2006
Gastprofessor, Universität Kaiserslautern, Germany, Spring, 1983
Head, Department of Mathematical Sciences, University of Cincinnati, l985 - 90
Visiting Fellow, Centre for Mathematical Analysis, Australian National University, Summer, l986
Visiting Member, Forschungsinstitut für Mathematik, ETH-Zurich, Switzerland, Fall, 1990.
Raybould Research Fellow, University of Queensland, Australia, Winter, 1996
Interim Dean, McMicken College of Arts and Sciences, University of Cincinnati, 2000-2001
Traubert Chair and Dean, School of Science and Mathematics, The Citadel, 2006-2011
Distinguished Professor of Mathematical Science, The Citadel, 2011-
ACTIVITIES
Editorial Boards:
Co-Editor: Journal of Integral Equations & Applications, 2002-08
Associate Editor: Numerical Functional Analysis and Optimization, 1986-,
SIAM Review 1992-96,
Electronic Journal of Differential Equations, 1992-,
Journal of Integral Equations & Applications, 1994-2008, 2009 -
Journal of Mathematical Analysis & Applications, 1996-2005
International Journal of Pure and Applied Mathematics, 2000-
Electronic Journal of Mathematical and Physical Sciences, 2002 –
Advisory Board, Scientific Journals International, 2008 -
Referee: For approximately 70 journals in mathematics, physics, computing, and
engineering.
Reviewer: SIAM Review, Mathematical Reviews, Computing Reviews, Zentralblatt
für Mathematik, Zeitschrift für Angewandte Mathematik und Mechanik,
Mathematics of Computation.
Organizer: U.C. Symposium on Numerical Analysis, May, l979 (co-organized with
J. T. King)
MAA (Ohio) Special Session on Approximations and Numerical Methods,
Spring, 1984
Alpine-U.S. Seminar on Inverse and Ill-posed Problems, St. Wolfgang,
Austria, June, l986 (co-organized with H. W. Engl)
CBMS Regional Conference on Fractal Geometry, Cincinnati, August, l987
(co-organized with K.R. Meyer)
NSF Faculty Enhancement Workshop on the Mathematics of Inverse Problems, Cincinnati, June,1992
MAA (Ohio) Special Session on Inverse Problems in the
Undergraduate Curriculum, Ohio Northern University, Fall, 1993
MAA Minicourse on Inverse Problems in the Classroom, 100th
Annual Meeting AMS, Cincinnati, January, 1994
Workshop on Ill-posed Problems for Graduate Students, Cincinnati,
June, 1994 (Co-organizer with D. Murio and T. King)
MAA (Ohio) Spring sectional meeting, University of Cincinnati, March, 2004
Chair: Institute for Mathematics and Its Applications Conference Selection Committee,
1988-89.
MAA George Polya Award Committee, 1995-98.
Member: Organizing Committee, IMA Industry Day, University of Chicago,
December,1989.
Presidential Young Investigator Panel, National Science Foundation,
Washington, D.C., 1989.
Committee of Visitors, Division of Mathematical Sciences, National
Science Foundation, Washington, D.C., 1990
Mathematical Association of America Consultant, 1991-95
National Research Council Department Chairs Panel on Implementation of the David II Report, 1990
SIAM Visiting Lecturers Program, 1995-
Joint Policy Board on Mathematics, Taskforce on Educational Activities of Faculty, 1995-99
MAA Visiting Lecturer, 1999-2004
National Advisory Committee, AASCU Project on Improving Mathematics Instruction for Teachers, 2000-2003
FELLOWSHIPS AND GRANTS
(PI=Principal Investigator, CPI=Co-investigator)
Air Force Office of Scientific Research Grant (PI), 1979-80
Science Research Council (Great Britain) Grant (CPI), 1980
National Science Foundation Grants (PI), l986-87, 1992-94, 1996-2000, (CPI) 2002-05
NATO Division of Scientific Affairs Grant (PI), 1993-96
Institute for Advanced Study Subcontract (NSF) (PI), 1997-2001, (CPI) 2003-2006
OBR - Eisenhower Professional Development Program (PI), 1998-99
OBR – Enhancing Teacher Quality Program (PI), 2000-2001
HONORS AND AWARDS
Exchange Scientist, National Academy of Sciences - Akademie der Wissenschaften der DDR, Spring, 1979
McMicken Award for Distinguished Scholarship, University of Cincinnati, 1991 (Inaugural research award among ~400 tenure line faculty)
Fellow of the Graduate School, University of Cincinnati, 1991- (lifetime appointment irrespective of affiliation)
George Pólya Award, Mathematical Association of America, 1994 (national award for expository excellence in mathematics)
Faculty Achievement Award, University of Cincinnati, 1994
Presidential Citation, for “Advancing the application of mathematics to science and industry”, Society for Industrial and Applied Mathematics, 1995
Decanal Citation, Universidad Nacional de Colombia, Sede Medellin, “por la importante contribcion academica a traves del cursillo ‘Problemas Inversos y Teoria de Operadores’”, 1998.
Sigma Pi Sigma (ΣΠΣ National Physics Honor Society, inducted 2011 in recognition of distinguished scholarship in physics)
Two special issues (Vol. 22, Nos. 2,3, 2010) of the Journal of Integral Equations and Applications dedicated by the Editors and authors to Charles Groetsch in recognition of “high regard for his contributions to the world of mathematics” and his “fundamental contributions to the field of inverse problems.”
Elected a Fellow of the American Association for the Advancement of Science (AAAS), 2010, in recognition of “distinguished contributions of the application of mathematics to science, particularly in the areas of inverse or ill-posed problems, approximation theory, and mathematical modeling.”
RESEARCH INTERESTS
Inverse and ill-posed problems, Integral Equations of the First Kind, Numerical Analysis, Approximation Theory, Applied Mathematics, Mathematics Pedagogy
PhD DISSERTATIONS SUPERVISED
(All at University of Cincinnati)
B. J. Jacobs, Topics in the approximation of generalized inverses, Ph.D., 1977.
Currently Honeywell Fellow (retired).
J. Guacaneme Dix, Aspects of the theory of Tikhonov's method for the numerical
solution of integral equations, Ph.D., 1984. Currently Professor of Mathematics, Texas State University.
G.D. Callon, Theory and approximation of the restricted pseudosolution, Ph.D.,
l986. Currently Professor of Mathematics, Franklin College.
INVITED LECTURES AT INTERNATIONAL SYMPOSIA
(Local Sponsor in parentheses)
Inverse and Improperly Posed Problems, Halle, E. Germany (Akademie der
Wissenschaften der DDR), June, 1979.
Nonlinear Analysis and Applications, St. Johns, Newfoundland (Canadian
National Research Council), June, 1981.
Treatment of Integral Equations by Numerical Methods, Durham, England (London
Mathematical Society), July, 1982.
Improperly Posed Problems and Their Numerical Treatment, Oberwolfach,
W. Germany, (Mathematisches Forschungsinstitut-Oberwolfach), October, 1982.
Centro Internazionale Matematico Estivo Conference on Inverse Problems,
Montecatini Terme, Italy (Consiglio Nazionale delle Ricerche), June, l986.
Practical Treatment of Integral Equations, Boundary Element Methods and
Singular Equations, Oberwolfach, W. Germany (Mathematisches
Forschungsinstitut-Oberwolfach), December, 1988
International Conference on Integral Equations and Inverse Problems,
Varna, Bulgaria (Bulgarian Academy of Sciences), September, 1989.
International Symposium on Inverse Problems in Engineering Sciences, Osaka,
Japan (Mathematical Society of Japan), August, 1990.
International Conference on Computational Mathematics, Matsuyama, Japan
(Ehime University, Japan Society for the Promotion of Science)
September, 1990
Workshop on Generalized Inverses, New Delhi, India (Indian Statistical
Institute) December, 1992
Second Hellenic-European Conference on Mathematics and Informatics, Athens,
Greece (Hellenic Mathematical Society), September, 1994
Third Southern Hemisphere Symposium on Undergraduate Mathematics Teaching, Berg en Dal, South Africa (African Mathematical Union; South African National Research Foundation), July, 2001
AMS/UMI Special Session on History of Mathematics, Pisa, Italy (Unione Matematica Italiana, Istituto Nazionale di Alta Matematica), June, 2002.
Inverse Problems in the Applied Sciences, Sapporo, Japan, (Japanese National Science Foundation), July, 2006
Tenth International Conference on Integral Methods in Science and Engineering, University of Cantabria, Santander, Spain (Ministerio de Educacion y Ciencia, Espana), July , 2008.
First Mexican Symposium on Inverse Problems and Applications, Ixtapa-Zihuatenejo, Mexico (Consejo Nacional de Ciencia y Technologia; Universidad Autónoma Metropolitana-Iztapalapa), January, 2010
COLLOQUIA & MAJOR LECTURES
University of Rhode Island, November, 1974
Boston University, March, 1975.
Brown University, May, 1975.
Idaho State University, February, 1976.
University of Rhode Island, February, 1976.
Air Force Institute of Technology, July, 1978.
Free University of Berlin, May, 1979.
Central Institute for Mathematics & Mechanics (E. Berlin), June, 1979.
University of Rostock, E. Germany, June, 1979.
Syracuse University, November, 1979.
University of Manchester, England, November, 1980.
Eidgenössische Technische Hochschule, Zurich, December, 1980.
Miami University, February, 1981.
University of Manchester, England, June, 1982.
University of Kaiserslautern, W. Germany, May, l983.
University of Frankfurt, W. Germany, May, 1983.
University of Florence, Italy, June, 1983.
University of Linz, Austria, June, 1983.
Iowa State University, April, l985.
Drake University (MAA Iowa Section SIAM Lecture) April, l985.
University of Puerto Rico, April, l985.
University of Melbourne, Australia, July, l986.
LaTrobe University, Australia, July, l986.
Centre for Mathematical Analysis, Canberra, Australia, August, l986.
Australian National University, August, l986.
University of New South Wales, Australia, August, l986.
Montana State University, October, l986.
Eastern Kentucky University, March, l987.
University of Klagenfurt, Austria, March, l987.
Wright State University, April,1988.
Northern Jiaotong University, Beijing, China, September,1988.
Peking University, Beijing, China, September, 1988.
Nankai Institute of Mathematics, Tianjin, China, September, 1988.
University of Graz, Austria, November, 1990
University of Munich, Germany, November, 1990
University of Göttingen, Germany, November, 1990.
University of Linz, Austria, November, 1990.
Eidgenössische Technische Hochschule, Zurich, November, 1990.
University of Louisville, April, 1991
Ball State University, November, 1991.
Eastern Kentucky University, March, 1992.
Ball State University, October, 1992.
National University of Singapore, December, 1992
Ohio Northern University, October, 1993
Kent State University, February, 1994
Bowling Green State University, April, 1994
University of Karlsruhe, Germany, July, 1994
Whitman College, November, 1994
Radford University, March, 1995
Boston College, September, 1995
University of Akron, October, 1995
University of Queensland, Australia, January & February, 1996
Colorado School of Mines, March, 1996
Rose-Hulman Institute of Technology, March, 1998
Universidad Nacional de Colombia, Medellin, September, 1998
Western Kentucky University, October, 1998
Tennessee Technological University, October, 1998
Bowling Green State University, March, 1999
Illinois State University, December, 1999
University of Kentucky, Lexington, February, 2000
Earlham College (IMAA Keynote Address), March, 2000
Ball State University, September, 2000
Xavier University, November, 2000 .
Calvin College, March, 2001
Michigan Epsilon Section, Pi Mu Epsilon, March, 2001
Western Michigan University, March, 2001
University of Tennessee, Knoxville, November, 2001
Baker University, February, 2002
Defiance College, March, 2002
Annual meeting of the Pacific Northwest Section MAA (Keynote Address), June, 2003
Southeastern Louisiana University, October, 2003
USMA-West Point, October, 2004
Michigan Technological University, October, 2004
Xavier University, April, 2005
Shawnee State University, May, 2005
Northern Kentucky University, February, 2006
Hokkaido University, Sapporo, Japan, July, 2006
College of Charleston, April, 2007
Northern Michigan University, April, 2008
University of Rhode Island, November, 2008
PUBLICATIONS
Books and Monographs
C.W. Groetsch, Generalized Inverses of Linear Operators: Representation and Approximation, Dekker, New York, 1977. ISBN 0-8247-6615-6
Charles Groetsch, Elements of Applicable Functional Analysis, Dekker, New York, 1980. ISBN 0-8247-6986-4
C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, London, 1984. ISBN 0-273-08642-1
J. Evans, C. W. Groetsch, and M. Walker, Fundamentals of Calculus: Applications to Managerial, Social and Life Sciences, West, St. Paul, l986. ISBN 0-314-93175-9
J. Evans, C. W. Groetsch, and M. Walker, An Introduction to Calculus: Methods and Applications, West, St. Paul, l986. ISBN 0-314-93176-7
C.W. Groetsch and J. Thomas King, Matrix Methods and Applications, Prentice-Hall, Englewood Cliffs, l988. ISBN 0-13-565565-X
H.W. Engl and C.W. Groetsch (Eds.), Inverse and Ill-Posed Problems, Academic Press,
Boston, l987. ISBN 0-12-239040-7
C.W. Groetsch, Inverse Problems in the Mathematical Sciences, Vieweg Verlag, Wiesbaden/Braunschweig, Germany, 1993. ISBN 3-528-06545-1
C.W. Groetsch, Inverse Problems in the Mathematical Sciences - Japanese translation by Kazuei Onishi, Kazumi Tanuma and Masahiro Yamamoto, Saiensu-sha, Tokyo, 1996. (Also appeared as a special edition of the Japanese journal Mathematical Sciences, June , 1996). ISBN 0-547-00619-1
C.W. Groetsch, Inverse Problems, Mathematical Association of America, Washington, D.C., 1999. ISBN 0-88385-716-2
C.W. Groetsch, Inverse Problems – Japanese translation by Akira Kaneko, Science Press, Tokyo, 2002. ISSN 0386-8257.
C.W. Groetsch, Inverse Problems – Mandarin Chinese translation by Jin Cheng, Yongji Tan and Jijun Liu, Springer, Beijing, 2006. Co-published by Tsinghua University Press, Biejing. ISBN 7-302-12713-1
C.W. Groetsch, Stable Approximate Evaluation of Unbounded Operators, LNM1894, Springer-Verlag, Heidelberg and Berlin, Germany, 2007, ISBN 3-540-39942-1
Published Articles (by sub-disciplinary category)
Integral Equations of the First Kind
C.W. Groetsch, Integral equations of the first kind, inverse problems and regularization, Journal of Physics: Conference Series 73(2007) 102001, 32 pp.
C.W. Groetsch, Some integral equations of the first kind in mechanics and regularization of ill-posed operator equations, in Inverse Problems in Engineering Science (M. Yamaguti et al, Eds.), Springer Verlag, Tokyo, 1991, pp.11-29.
C.W. Groetsch, Convergence analysis of a regularized degenerate kernel method for Fredholm integral equations of the first kind, Integral Equations and Operator Theory 13(1990), 67-75
C.W. Groetsch and J. Guacaneme, Arcangeli's method for Fredholm equations of the first kind, Proceedings of the American Mathematical Society, 99(l987), 256-26l.
C.W. Groetsch, Uniform convergence of regularization methods for Fredholm equations of the first kind, Journal of the Australian Mathematical Society 39(1985) 282-286.
C.W. Groetsch and J. Guacaname, On regularized Ritz approximations for Fredholm equations of the first kind, Rocky Mountain Journal of Mathematics 15(l985), 33-39.
Also appeared as Publication No. l0, Istituto di Analisi Globale e Applicazioni, CNR, Florence, Italy, l983.
C.W. Groetsch, J.T. King and D.A. Murio, Asymptotic analysis of a finite element method for Fredholm equations of the first kind, Numerical Treatment of Integral Equations (C.T.H. Baker, Ed.) Academic Press, London, 1982, pp. 1-11.
C.W. Groetsch, On a regularization-Ritz method for Fredholm equations of the first kind, Journal of Integral Equations 4 (1982), 1973-182.
C.W. Groetsch, On existence criteria and approximation procedures for integral equations of the first kind, Mathematics of Computation 29 (1975), 1105-1108.
Inverse and Ill-posed Problems
C.W. Groetsch, Linear inverse problems, pp. 3-41, Chapter I in Handbook of Mathematical Methods in Imaging (O. Scherzer, Univ. Vienna, Ed.), Springer, New York, 2011.
C.W. Groetsch, Inverse problems: the other two-thirds of the story, Quaestiones Mathematicae 24(2001), Supplement 1, 89-94.
C.W. Groetsch, Regularization and stabilization of inverse problems, Chapter 2 in Handbook of Analytic- Computational Methods in Applied Mathematics, Chapman and Hall, Boca Raton, 2000, pp. 31-64.
C.W. Groetsch, Tartaglia's inverse problem in a resistive medium, The American Mathematical Monthly 103(1996), 546-551.
C.W. Groetsch, Spectral methods for linear inverse problems with unbounded operators, Journal of Approximation Theory 70(1992), 16-28.
C.W. Groetsch and E. Schock, Asymptotic convergence rate for Arcangeli's method for ill-posed problems, Applicable Analysis l8 (l984), l75-l82.
C.W. Groetsch, Comments on Morozov's discrepancy principle, Improperly Posed Problems and their Numerical Treatment (G. Hämmerlin & K. Hoffmann, Eds.), Birkhauser, Basel, 1983, pp. 97-104.
C.W. Groetsch, On the Kryanev-Lardy method for ill-posed problems, Mathematisches Nachrichten 96(1980), 27-31
Regularization Theory
C.W. Groetsch, Tikhonov-Phillips regularization, Encyclopaedia of Mathematics, Supplement II, Kluwer, Dordrecht, 2000, pp. 462-464.
Martin Hanke and C.W. Groetsch, Nonstationary iterated Tikhonov regularization, Journal of Optimization Theory and Applications 98(1998), 37-53.
C.W. Groetsch and M. Hanke, Regularization by projection of unbounded operators arising in inverse problems, in Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology (D.D. Ang, et al., Eds.), pp. 61-70, Publications of the HoChiMinh City Mathematical Society, vol.2, HoChiMinh City, 1995.
C.W. Groetsch and A. Neubauer, Regularization of ill-posed problems: Optimal parameter choice in finite dimensions, Journal of Approximation Theory 58(1989), 184-201.
H.W. Engl and C.W. Groetsch, A higher order approximate method for restricted linear least squares problems, Bulletin of the Australian Mathematical Society 37(l988) l2l-l30.
C.W. Groetsch and C.R. Vogel, Asymptotic theory of filtering for linear operator equations with discrete noisy data, Mathematics of Computation 49 (l987), 499-506.
H.W. Engl and C.W. Groetsch, Projection-regularization methods for linear operator equations of the first kind, Proceedings of the Centre for Mathematical Analysis (Canberra), 17(1988), 17-31.