List of Titles

Authors: Briquel, Irenee , Cucker, Felipe , Peña, Javier , Roshchina, Vera
Date: 2014
Type: Text , Journal article
Relation: Mathematics of Computation Vol. 83, no. 287 (2014), p. 1279-1317
Full Text: false
Reviewed:
Description: A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite precision. In this paper we describe a finite-precision version of this algorithm. Our main result shows that this version works within the same time bounds and requires a precision which, on the average, amounts to a polynomial amount of bits in the mantissa of the intervening floating-point numbers. © 2013 American Mathematical Society.

Authors: Cucker, Felipe , Peña, Javier , Roshchina, Vera
Date: 2014
Type: Text , Journal article
Relation: Mathematical Programming Vol. 150, no. 2 (2014), p. 217-250
Full Text: false
Reviewed:
Description: We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited. © 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

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