Reliable implementation of real number algorithms

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A significant portion of modern computer capacity is dedicated to computations involving real numbers, which present unique challenges, particularly in ensuring verified or reliable computations. Real numbers contain infinite information, making precise representation on computers impossible and leading to issues with unverified implementations of algorithms that use finite precision. While often viewed as a numerical mathematics issue, various scientific communities within computer science also confront this challenge. This book stems from the Dagstuhl Seminar 06021 on “Reliable Implementation of Real Number Algorithms: Theory and Practice,” held from January 8–13, 2006. The seminar aimed to foster dialogue among diverse communities addressing the reliable implementation of real number algorithms from both theoretical and practical perspectives. Forty-eight researchers from various countries and disciplines convened at Dagstuhl Castle to share insights in a relaxed setting. The program featured 35 talks, each lasting 30 minutes, along with three evening sessions for additional presentations and discussions. Engaging conversations emerged regarding different theoretical models and practical approaches for achieving reliable real number computations.