Floating-point arithmetic on the test bench. How are verified numerical solutions calculated?
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Publication:335016
DOI10.1365/s13291-016-0138-1zbMath1372.65140OpenAlexW2429814779MaRDI QIDQ335016
Publication date: 2 November 2016
Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1365/s13291-016-0138-1
Interval and finite arithmetic (65G30) Algorithms with automatic result verification (65G20) Numerical algorithms for computer arithmetic, etc. (65Y04)
Related Items (2)
Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin's \(\sin (\theta)\) theorem ⋮ Mathematically rigorous global optimization in floating-point arithmetic
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Cites Work
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- The SIAM 100-Digit Challenge: a decade later. Inspirations, ramifications, and other eddies left in its wake
- A generalization of \(p\)-boxes to affine arithmetic
- Interactive theorem proving and program development. Coq'Art: the calculus of inductive constructions. Foreword by Gérard Huet and Christine Paulin-Mohring.
- Error estimation of floating-point summation and dot product
- Error analysis of floating-point computation
- Inversion of extremely ill-conditioned matrices in floating-point
- Symmetry and related properties via the maximum principle
- Adaptive precision floating-point arithmetic and fast robust geometric predicates
- Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
- Rump's example revisited
- A polyhedral branch-and-cut approach to global optimization
- Accurate solution of dense linear systems I: Algorithms in rounding to nearest
- Affine arithmetic: concepts and applications
- A floating-point technique for extending the available precision
- The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?
- Improved Error Bounds for Inner Products in Floating-Point Arithmetic
- Verification methods: Rigorous results using floating-point arithmetic
- Improved Backward Error Bounds for LU and Cholesky Factorizations
- HOL Light: An Overview
- Average-Case Stability of Gaussian Elimination
- MPFR
- Pitfalls of a Full Floating-Point Proof: Example on the Formal Proof of the Veltkamp/Dekker Algorithms
- Rigorous Error Bounds for the Optimal Value in Semidefinite Programming
- Handbook of Floating-Point Arithmetic
- Iterative Refinement Implies Numerical Stability for Gaussian Elimination
- Gaussian Elimination with Partial Pivoting Can Fail in Practice
- On the Sensitivity of Solution Components in Linear Systems of Equations
- Algorithm 755: ADOL-C
- A mathematical view of automatic differentiation
- Large Growth Factors in Gaussian Elimination with Pivoting
- Accuracy and Stability of Numerical Algorithms
- The SIAM 100-Digit Challenge
- Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen
- A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable
- Theorem Proving in Higher Order Logics
- The Problem of Integration in Finite Terms
- Some Comments from a Numerical Analyst
- Modern Error Analysis
- Accurate Sum and Dot Product
- Numerical inverting of matrices of high order
- ROUNDING-OFF ERRORS IN MATRIX PROCESSES
- Some New Methods in Matrix Calculation
- Numerical linear algebra. A concise introduction with MATLAB and Julia
- A remarkable example of catastrophic cancellation unraveled
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