On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots
DOI10.1553/etna_vol55s401zbMath1487.65052OpenAlexW3207518756MaRDI QIDQ2672185
Thomas R. Cameron, Stef Graillat
Publication date: 8 June 2022
Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1553/etna_vol55s401
polynomial rootspolynomial evaluationbackward errorrounding error analysisforward errorerror-free transformations
Complexity and performance of numerical algorithms (65Y20) Numerical computation of roots of polynomial equations (65H04) Software, source code, etc. for problems pertaining to numerical analysis (65-04)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems
- Accurate evaluation of a polynomial and its derivative in Bernstein form
- Numerical computation of polynomial zeros by means of Aberth's method
- Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic
- Algorithms for accurate, validated and fast polynomial evaluation
- Accurate simple zeros of polynomials in floating point arithmetic
- Accurate evaluation of the \(k\)-th derivative of a polynomial and its application
- A posteriori error bounds for the zeros of polynomials
- A floating-point technique for extending the available precision
- Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems
- Ultimately Fast Accurate Summation
- MPFR
- Accurate and Efficient Floating Point Summation
- Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
- Accuracy and Stability of Numerical Algorithms
- Lectures on Finite Precision Computations
- Accurate Floating-Point Summation Part I: Faithful Rounding
- Quasi double-precision in floating point addition
- Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit
- A modified Newton method for polynomials
- Accurate Sum and Dot Product
This page was built for publication: On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots