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Algorithms for accurate, validated and fast polynomial evaluation
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/bf01397083openalex-snapshot
A floating-point technique for extending the available precision
inferredcites →https://doi.org/10.1016/j.cam.2003.08.017openalex-snapshot
More accuracy at fixed precision
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How to Ensure a Faithful Polynomial Evaluation with the Compensated Horner Algorithm
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Accurate Floating-Point Summation Part I: Faithful Rounding
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Accuracy and Stability of Numerical Algorithms
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Applied Numerical Linear Algebra
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Improving the compensated Horner scheme with a fused multiply and add
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Design, implementation and testing of extended and mixed precision BLAS
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Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit
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The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
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Residual iteration and accurate polynomial evaluation for shape-interrogation applications
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Accuracy and stability of numerical algorithms
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Applied numerical linear algebra
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Automatic source‐to‐source error compensation of floating‐point programs: code synthesis to optimize accuracy and time
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Enhanced Floating-Point Sums, Dot Products, and Polynomial Values
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Parallel Accurate and Reproducible Summation
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An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods
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A Compensated Estrin Scheme for Accurate Polynomial Evaluation
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Efficient and Accurate Evaluation of Bézier Tensor Product Surfaces
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Evaluation schemes in the ring of quaternionic polynomials
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High-precision computation: Mathematical physics and dynamics
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Accurate quotient-difference algorithm: Error analysis, improvements and applications
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Numerical validation of compensated algorithms with stochastic arithmetic
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Compensated de Casteljau algorithm in K times the working precision
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PACF: A precision-adjustable computational framework for solving singular values
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Accurate evaluation algorithm for bivariate polynomial in Bernstein–Bézier form
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Reducing rounding errors and achieving Brouwerʼs law with Taylor Series Method
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Matrix representations for multi-degree B-splines
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Accurate evaluation of a polynomial and its derivative in Bernstein form
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Augmented Precision Square Roots and 2-D Norms, and Discussion on Correctly Rounding sqrt(x^2+y^2)
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Accurate and Fast Evaluation of Elementary Symmetric Functions
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Alternative Split Functions and Dekker’s Product
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Shadow computation with BFloat16 to estimate the numerical accuracy of summations
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A parallel compensated Horner scheme for SIMD architecture
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Automatic Source-to-Source Error Compensation of Floating-Point Programs
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Compensated Algorithm for Evaluating the Derivative of Bézier Tensor Product Surface
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Some Accurate Methods for Finding Simple Roots of Polynomials in Floating Point Arithmetic
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Notice of Retraction: Accurate Evaluation the Derivative of a Polynomial
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Design and Implementation of Mixed Extended-Precision Package in MATLAB
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Accurate Evaluation of Bivariate Polynomials
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Tight Interval Inclusions with Compensated Algorithms
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Quotient-Difference Algorithm and Code for Cubic Polynomials with Computational Implementation
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On the sum-of-products to product-of-sums transformation between analytical low-rank approximations in finite basis representation
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On the Robustness of the 2Sum and Fast2Sum Algorithms
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Accurate Evaluation of Polynomials in Legendre Basis
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On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots
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Accurate Goertzel Algorithm: Error Analysis, Validations and Applications
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Compensated Evaluation of Tensor Product Surfaces in CAGD
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Optimisation de la précision numérique des codes parallèles
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Tools for the Design of Reliable and Efficient Functions Evaluation Libraries
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Amélioration de la fiabilité numérique de codes de calcul industriels
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