Mathematical Sciences: Dynamical Systems and Complexity
{'Code': '03040108', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
The main objectives of this project are to enhance the                     understanding of dynamical systems, to study the relation of                    these dynamical systems to topology and to algorithms in                        numerical analysis, and to study the global geometric properties                of these algorithms and their computational process.  The                       principal investigator proposes a theory of computation and a                   model for computation over the real numbers.  This theory                       includes recursive function theory, universal machines, and NP                  completeness.  For example, degenerate fixed points occur in the                analysis of the iterative processes for polynomial root finding                 and interior point methods for linear programming.  Blowing up                  techniques for the linear programming problem involve the                       dynamics of the n-sphere.  An understanding of this problem has                 implications for the asymptotic rate of attraction to the optima                for discrete versions of the linear and the projective rescaling                algorithms of linear programming.
{'FirstName': 'Michael', 'LastName': 'Shub', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Michael Shub', 'EmailAddress': 'shub.michael@gmail.com', 'NSF_ID': '000119032', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'IBM Thomas J Watson Research Center', 'CityName': 'YORKTOWN HEIGHTS', 'ZipCode': '10598', 'PhoneNumber': '7137974625', 'StreetAddress': '1101 KITCHAWAN RD', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '17', 'CONGRESS_DISTRICT_ORG': 'NY17', 'ORG_UEI_NUM': 'EDHQH5AXXQZ5', 'ORG_LGL_BUS_NAME': 'INTERNATIONAL BUSINESS MACHINES CORP', 'ORG_PRNT_UEI_NUM': 'J64CSQTQNRC1'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1989&All=true', 'xml': '8900443.xml'}