Preconditioners for the interval Gauss-Seidel method
SIAM Journal on Numerical Analysis
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Handling floating-point exceptions in numeric programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
How do you solve a quadratic equation?
How do you solve a quadratic equation?
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
The design of the Boost interval arithmetic library
Theoretical Computer Science - Real numbers and computers
FILIB++, a fast interval library supporting containment computations
ACM Transactions on Mathematical Software (TOMS)
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The algorithm that computes the midpoint of an interval with floating-point bounds requires some careful devising to handle all possible inputs correctly. We review several implementations from prominent C/C++ interval arithmetic packages and analyze their potential failure to deliver the expected results. We then show how to amend them to avoid common pitfalls. The results presented are also relevant to noninterval arithmetic computation such as the implementation of bisection methods. Enough background on IEEE 754 floating-point arithmetic is provided for this article to serve as a practical introduction to the analysis of floating-point computation.