A New Approach to Probabilistic Rounding Error Analysis
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Publication:5238758
DOI10.1137/18M1226312WikidataQ127240913 ScholiaQ127240913MaRDI QIDQ5238758
Theo A. Mary, Nicholas J. Higham
Publication date: 28 October 2019
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
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- Reducing Floating Point Error in Dot Product Using the Superblock Family of Algorithms
- Probabilistic error analysis of Gaussian elimination in floating point and logarithmic arithmetic
- Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
- Weighing the Odds
- Improved Error Bounds for Inner Products in Floating-Point Arithmetic
- Improved Backward Error Bounds for LU and Cholesky Factorizations
- The university of Florida sparse matrix collection
- A Stochastic Roundoff Error Analysis for the Fast Fourier Transform
- Error Analysis of Direct Methods of Matrix Inversion
- Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions
- Accuracy and Stability of Numerical Algorithms
- Simulating Low Precision Floating-Point Arithmetic
- Probability Inequalities for Sums of Bounded Random Variables
- Tests of probabilistic models for propagation of roundoff errors
- Test of probabilistic models for the propagation of roundoff errors
- A statistical model of roundoff error for varying length floating-point arithmetic
- Numerical inverting of matrices of high order
