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Ultimately Fast Accurate Summation
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/zamm.19740540106openalex-snapshot
Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen
inferredcites →https://doi.org/10.1007/bf01397083openalex-snapshot
A floating-point technique for extending the available precision
inferredcites →https://doi.org/10.1007/bf01404922openalex-snapshot
Correction d'une somme en arithmetique a virgule flottante
inferredcites →https://doi.org/10.1007/bf02253892openalex-snapshot
Least significant bit evaluation of arithmetic expressions in single-precision
inferredcites →https://doi.org/10.1007/pl00009321openalex-snapshot
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates
inferredcites →https://doi.org/10.1007/s002110100310openalex-snapshot
Fast verification of solutions of matrix equations
inferredcites →https://doi.org/10.1109/12.589241openalex-snapshot
Validated roundings of dot products by sticky accumulation
inferredcites →https://doi.org/10.1109/arith.1991.145549openalex-snapshot
Algorithms for arbitrary precision floating point arithmetic
inferredcites →https://doi.org/10.1137/030602009openalex-snapshot
A New Distillation Algorithm for Floating-Point Summation
inferredcites →https://doi.org/10.1137/050645671openalex-snapshot
Accurate Floating-Point Summation Part I: Faithful Rounding
inferredcites →https://doi.org/10.1137/07068816xopenalex-snapshot
Accurate Floating-Point Summation Part II: Sign, K -Fold Faithful and Rounding to Nearest
inferredcites →https://doi.org/10.1137/0914050openalex-snapshot
The Accuracy of Floating Point Summation
inferredcites →https://doi.org/10.1137/s1052623402401804openalex-snapshot
Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization
inferredcites →https://doi.org/10.1137/s1064827502407627openalex-snapshot
Accurate and Efficient Floating Point Summation
inferredcites →https://doi.org/10.1145/1141277.1141585openalex-snapshot
Improving the compensated Horner scheme with a fused multiply and add
inferredcites →https://doi.org/10.1145/1141277.1141586openalex-snapshot
Provably faithful evaluation of polynomials
inferredcites →https://doi.org/10.1145/1390768.1390792openalex-snapshot
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
inferredcites →https://doi.org/10.1145/362854.362889openalex-snapshot
On accurate floating-point summation
inferredcites →https://doi.org/10.1145/567806.567808openalex-snapshot
Design, implementation and testing of extended and mixed precision BLAS
inferredcites →https://doi.org/10.2172/817634openalex-snapshot
ARPREC: An arbitrary precision computation package
inferredcites →https://doi.org/10.5860/choice.34-0981openalex-snapshot
Accuracy and stability of numerical algorithms
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Error‐free transformation of matrix multiplication with a posteriori validation
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Enhanced Floating-Point Sums, Dot Products, and Polynomial Values
inferred← citeshttps://doi.org/10.1007/978-3-030-80119-9_21openalex-snapshot
Parallel Accurate and Reproducible Summation
inferred← citeshttps://doi.org/10.1007/978-3-030-95561-8_10openalex-snapshot
An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods
inferred← citeshttps://doi.org/10.1007/978-3-319-31769-4_8openalex-snapshot
Efficiency of Reproducible Level 1 BLAS
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Exploiting Structure in Floating-Point Arithmetic
inferred← citeshttps://doi.org/10.1007/978-3-319-58943-5_49openalex-snapshot
Reproducible, Accurately Rounded and Efficient BLAS
inferred← citeshttps://doi.org/10.1007/978-3-319-76526-6_5openalex-snapshot
Enhanced Floating-Point Sums, Dot Products, and Polynomial Values
inferred← citeshttps://doi.org/10.1007/978-3-642-28145-7_15openalex-snapshot
Comments on Fast and Exact Accumulation of Products
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PerPI: A Tool to Measure Instruction Level Parallelism
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The stability of barycentric interpolation at the Chebyshev points of the second kind
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A note on Dekker’s FastTwoSum algorithm
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Error estimation of floating-point summation and dot product
inferred← citeshttps://doi.org/10.1007/s11075-011-9478-1openalex-snapshot
Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications
inferred← citeshttps://doi.org/10.1007/s13160-024-00677-zopenalex-snapshot
Extension of accurate numerical algorithms for matrix multiplication based on error-free transformation
inferred← citeshttps://doi.org/10.1007/s42514-023-00150-2openalex-snapshot
ddRingAllreduce: a high-precision RingAllreduce algorithm
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Meshless weighting coefficients for arbitrary nodes: The efficient computation to machine precision using hyper-dual numbers
inferred← citeshttps://doi.org/10.1016/j.amc.2015.08.134openalex-snapshot
Accurate, validated and fast evaluation of elementary symmetric functions and its application
inferred← citeshttps://doi.org/10.1016/j.cam.2012.10.010openalex-snapshot
Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest
inferred← citeshttps://doi.org/10.1016/j.cam.2015.04.010openalex-snapshot
Improvement of error-free splitting for accurate matrix multiplication
inferred← citeshttps://doi.org/10.1016/j.laa.2012.07.001openalex-snapshot
Fast enclosure for solutions of Sylvester equations
inferred← citeshttps://doi.org/10.1016/j.parco.2014.04.007openalex-snapshot
An order-invariant real-to-integer conversion sum
inferred← citeshttps://doi.org/10.1016/j.parco.2015.09.001openalex-snapshot
Numerical reproducibility for the parallel reduction on multi- and many-core architectures
inferred← citeshttps://doi.org/10.1016/j.parco.2019.04.002openalex-snapshot
Full-neighbor-list based numerical reproducibility method for parallel molecular dynamics simulations
inferred← citeshttps://doi.org/10.1016/j.parco.2023.102996openalex-snapshot
Multi-level parallel multi-layer block reproducible summation algorithm
inferred← citeshttps://doi.org/10.1017/s096249291000005xopenalex-snapshot
Verification methods: Rigorous results using floating-point arithmetic
inferred← citeshttps://doi.org/10.1109/access.2020.2982365openalex-snapshot
Using Floating-Point Intervals for Non-Modular Computations in Residue Number System
inferred← citeshttps://doi.org/10.1109/arith.2013.18openalex-snapshot
Accurate and Fast Evaluation of Elementary Symmetric Functions
inferred← citeshttps://doi.org/10.1109/arith.2013.19openalex-snapshot
Accurate Parallel Floating-Point Accumulation
inferred← citeshttps://doi.org/10.1109/arith.2013.43openalex-snapshot
Numerical Reproducibility and Accuracy at ExaScale
inferred← citeshttps://doi.org/10.1109/arith.2013.9openalex-snapshot
Fast Reproducible Floating-Point Summation
inferred← citeshttps://doi.org/10.1109/arith.2016.18openalex-snapshot
A New Multiplication Algorithm for Extended Precision Using Floating-Point Expansions
inferred← citeshttps://doi.org/10.1109/arith.2016.9openalex-snapshot
Correctly Rounded Arbitrary-Precision Floating-Point Summation
inferred← citeshttps://doi.org/10.1109/arith.2018.8464793openalex-snapshot
On Various Ways to Split a Floating-Point Number
inferred← citeshttps://doi.org/10.1109/arith.2018.8464813openalex-snapshot
Augmented Arithmetic Operations Proposed for IEEE-754 2018
inferred← citeshttps://doi.org/10.1109/codit.2016.7593626openalex-snapshot
Data-types optimization for floating-point formats by program transformation
inferred← citeshttps://doi.org/10.1109/correctness51934.2020.00011openalex-snapshot
A Statistical Analysis of Error in MPI Reduction Operations
inferred← citeshttps://doi.org/10.1109/hpcc.2014.204openalex-snapshot
Numerical Verification of Large Scale CFD Simulations: One Way to Prepare the Exascale Challenge
inferred← citeshttps://doi.org/10.1109/icis.2016.7550817openalex-snapshot
Parallel online exact sum for Java8
inferred← citeshttps://doi.org/10.1109/ipdps.2014.127openalex-snapshot
Designing Bit-Reproducible Portable High-Performance Applications
inferred← citeshttps://doi.org/10.1109/ipdps.2016.41openalex-snapshot
Order-Invariant Real Number Summation: Circumventing Accuracy Loss for Multimillion Summands on Multiple Parallel Architectures
inferred← citeshttps://doi.org/10.1109/ntms.2015.7266509openalex-snapshot
Numerical reproducibility: Feasibility issues
inferred← citeshttps://doi.org/10.1109/sa47457.2019.8938060openalex-snapshot
How orthogonal are we? A note on fast and accurate inner product computation in the floating-point arithmetic
inferred← citeshttps://doi.org/10.1109/tc.2014.2345391openalex-snapshot
Parallel Reproducible Summation
inferred← citeshttps://doi.org/10.1109/tc.2016.2532874openalex-snapshot
Accurate Parallel Floating-Point Accumulation
inferred← citeshttps://doi.org/10.1109/tc.2017.2690632openalex-snapshot
Correctly Rounded Arbitrary-Precision Floating-Point Summation
inferred← citeshttps://doi.org/10.1109/tc.2020.3002702openalex-snapshot
Emulating Round-to-Nearest Ties-to-Zero “Augmented” Floating-Point Operations Using Round-to-Nearest Ties-to-Even Arithmetic
inferred← citeshttps://doi.org/10.1137/24m1647217openalex-snapshot
Condense and Distill: Fast Distillation of Large Floating-Point Sums via Condensation
inferred← citeshttps://doi.org/10.1145/2457443.2457444openalex-snapshot
Self-Alignment Schemes for the Implementation of Addition-Related Floating-Point Operators
inferred← citeshttps://doi.org/10.1145/2699469openalex-snapshot
Efficient Calculations of Faithfully Rounded l 2 -Norms of n -Vectors
inferred← citeshttps://doi.org/10.1145/2785965openalex-snapshot
IEEE754 Precision- k base-β Arithmetic Inherited by Precision- m Base-β Arithmetic for k < m
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Algorithms for Efficient Reproducible Floating Point Summation
inferred← citeshttps://doi.org/10.1145/3563353openalex-snapshot
Fast shadow execution for debugging numerical errors using error free transformations
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Correctly Rounded Math Libraries without Worrying about the Application’s Rounding Mode
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Hierarchical approach for deriving a reproducible unblocked LU factorization
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Full-Speed Deterministic Bit-Accurate Parallel Floating-Point Summation on Multi- and Many-Core Architectures
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Analytic integration of the Newton potential over cuboids and an application to fast multipole methods
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On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots
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УРОВЕНЬ АРХИТЕКТУРЫ МИКРОКОМАНД С ДЛИННОЙ ДВОИЧНОЙ АРИФМЕТИКОЙ ДЛЯ КОМПЬЮТЕРНОЙ СИСТЕМЫ ВЫСОКОТОЧНЫХ ВЫЧИСЛЕНИЙ
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Parallel Online Exact Summation of Floating-point Numbers by Applying MapReduce of Java8
inferred← citeshttps://doi.org/10.5220/0004884802040214openalex-snapshot
Code Size and Accuracy-aware Synthesis of Fixed-point Programs for Matrix Multiplication
inferred← citeshttps://doi.org/10.52547/mmr.7.2.389openalex-snapshot
Numerical Stability in Complex Summation
inferred← citeshttps://doi.org/10.55630/sjc.2010.4.349-370openalex-snapshot
Extension of the C-XSC Library with Scalar Products with Selectable Accuracy
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Optimisation de la précision numérique des codes parallèles
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Efficient computation with structured matrices and arithmetic expressions
inferred← citeshttps://doi.org/10.70675/3deecc49zba51z4288z9b40zaec4f9cd7f8eopenalex-snapshot
Towards fast and certified multiple-precision librairies
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How to improve the numerical reproducibility of hydrodynamics simulations : analysis and solutions for one open-source HPC software
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Towards reproducible, accurately rounded and efficient BLAS
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