Global Convergence of Hessenberg Shifted QR II: Finite Arithmetic: Global convergence of Hessenberg shifted QR. II: Finite arithmetic

Authors: Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava

Source: SIAM Journal on Matrix Analysis and Applications. 46:1168-1211

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical algorithms for computer arithmetic, etc, shifted QR, numerical linear algebra, Ritz values, nonnormality, dynamical systems

File Description: application/xml

Retraction: The algorithmic numbers in non-archimedean numerical computing environments 'The status of this article has been Retraction: Discrete and Continuous Dynamical Systems - S, 18 (2025), 2063-2063, doi: 10.3934/dcdss.2025063': The algorithmic numbers in non-Archimedean numerical computing environments

Authors: Benci, Vieri, Cococcioni, Marco

Source: Discrete and Continuous Dynamical Systems - S. 14:1673-1692

Subject Terms: fixed-length formats, 4. Education, Nonstandard models in mathematics, 02 engineering and technology, nonstandard analysis, Nonstandard analysis, 01 natural sciences, Infinitesimal numbers, Nonstandard Analysis, Euclidean numbers, Non-Archimedean Scientitic Computing, Fixed-length formats, Hardware-friendly Representations, Euclidean numbers, hardware-friendly representations, Numerical algorithms for computer arithmetic, etc, non-Archimedean scientific computing, 0202 electrical engineering, electronic engineering, information engineering, infinitesimal numbers, Non-Archimedean analysis, 0101 mathematics

File Description: application/xml

Access URL: https://www.aimsciences.org/article/exportPdf?id=0d97e516-efaa-407f-b95b-c7fc523eba84
https://zbmath.org/7439617
https://doi.org/10.3934/dcdss.2020449
https://www.aimsciences.org/article/exportPdf?id=0d97e516-efaa-407f-b95b-c7fc523eba84
https://www.aimsciences.org/article/doi/10.3934/dcdss.2020449

A new architecture for a parallel finite field multiplier with low complexity based on composite fields: A new architecture for a parallel finite field multiplier with low complexity based on composite fields.

Authors: Christof Paar

Source: IEEE Transactions on Computers. 45:856-861

Subject Terms: polynomial multiplication, VLSI architecture, Numerical algorithms for computer arithmetic, etc, Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.), bit parallel multiplication, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, Karatsuba Ofman algorithm, Mathematical problems of computer architecture

File Description: application/xml

Access URL: https://zbmath.org/1966814
https://doi.org/10.1109/12.508323

Sieving Procedures on a Digital Computer: Sieving procedures on a digital computer

Authors: Marvin C. Wunderlich

Source: Journal of the ACM. 14:10-19

Subject Terms: Primality, sieve methods, Numerical algorithms for computer arithmetic, etc, sieving procedures, Factorization

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/jacm/jacm14.html#Wunderlich67
https://dl.acm.org/doi/10.1145/321371.321373

Group carry asynchronous adder in digital computers

Authors: Yang, Si-zen, Lee, Le

Subject Terms: Numerical algorithms for computer arithmetic, etc, numerical analysis

File Description: application/xml

Access URL: https://zbmath.org/3231586