TY - GEN
T1 - Analytic root clustering
T2 - 9th Conference on Computability in Europe - The Nature of Computation: Logic, Algorithms, Applications, CiE 2013
AU - Yap, Chee
AU - Sagraloff, Michael
AU - Sharma, Vikram
PY - 2013
Y1 - 2013
N2 - A challenge to current theories of computing in the continua is the proper treatment of the zero test. Such tests are critical for extracting geometric information. Zero tests are expensive and may be uncomputable. So we seek geometric algorithms based on a weak form of such tests, called soft zero tests. Typically, algorithms with such tests can only determine the geometry for "nice" (e.g., non-degenerate, non-singular, smooth, Morse, etc) inputs. Algorithms that avoid such niceness assumptions are said to be complete. Can we design complete algorithms with soft zero tests? We address the basic problem of determining the geometry of the roots of a complex analytic function f. We assume effective box functions for f and its higher derivatives are provided. The problem is formalized as the root clustering problem, and we provide a complete (δ,∈)-exact algorithm based on soft zero tests.
AB - A challenge to current theories of computing in the continua is the proper treatment of the zero test. Such tests are critical for extracting geometric information. Zero tests are expensive and may be uncomputable. So we seek geometric algorithms based on a weak form of such tests, called soft zero tests. Typically, algorithms with such tests can only determine the geometry for "nice" (e.g., non-degenerate, non-singular, smooth, Morse, etc) inputs. Algorithms that avoid such niceness assumptions are said to be complete. Can we design complete algorithms with soft zero tests? We address the basic problem of determining the geometry of the roots of a complex analytic function f. We assume effective box functions for f and its higher derivatives are provided. The problem is formalized as the root clustering problem, and we provide a complete (δ,∈)-exact algorithm based on soft zero tests.
UR - http://www.scopus.com/inward/record.url?scp=84880397975&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880397975&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-39053-1_51
DO - 10.1007/978-3-642-39053-1_51
M3 - Conference contribution
AN - SCOPUS:84880397975
SN - 9783642390524
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 434
EP - 444
BT - The Nature of Computation
Y2 - 1 July 2013 through 5 July 2013
ER -