scholarly journals An Improvement of Cyclic Vector Multiplication Algorithm

10.5772/9639 ◽  
2010 ◽  
Author(s):  
Hidehiro Kato ◽  
Yasuyuki Nogami ◽  
Tomoki Yoshida ◽  
Kenta Nekado ◽  
Shoichi Takeuchi ◽  
...  
Keyword(s):  
Cyclic Vector ◽  
Multiplication Algorithm

Cyclic Vector Multiplication Algorithm and Existence Probability of Gauss Period Normal Basis

2011 ◽  
Vol E94-A (1) ◽  
pp. 172-179 ◽  
Author(s):  
Kenta NEKADO ◽  
Yasuyuki NOGAMI ◽  
Hidehiro KATO ◽  
Yoshitaka MORIKAWA
Keyword(s):  
Normal Basis ◽  
Cyclic Vector ◽  
Gauss Period ◽  
Multiplication Algorithm ◽  
Existence Probability

scholarly journals Cyclic Vector Multiplication Algorithm Based on a Special Class of Gauss Period Normal Basis

ETRI Journal ◽  
2007 ◽  
Vol 29 (6) ◽  
pp. 769-778 ◽  
Author(s):  
Hidehiro Kato ◽  
Yasuyuki Nogami ◽  
Tomoki Yoshida ◽  
Yoshitaka Morikawa
Keyword(s):  
Special Class ◽  
Normal Basis ◽  
Cyclic Vector ◽  
Gauss Period ◽  
Multiplication Algorithm

scholarly journals An Improvement of Cyclic Vector Multiplication Algorithm

2008 ◽  
Author(s):  
Hidehiro Kato ◽  
Yasuyuki Nogami ◽  
Tomoki Yoshida ◽  
Kenta Nekado ◽  
Shoichi Takeuchi ◽  
...  
Keyword(s):  
Cyclic Vector ◽  
Multiplication Algorithm

A Brief Study and An Arduino Based Implementation of Booths Multiplication Algorithm

2019 ◽  
Vol 7 (6) ◽  
pp. 307-313
Author(s):  
Kushankur Ghosh ◽  
Arghasree Banerjee
Keyword(s):  
Multiplication Algorithm

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

An Efficient Signed Digit Montgomery Modular Multiplication Algorithm

2021 ◽  
pp. 105099
Author(s):  
ShiLei Zhao ◽  
Hai Huang ◽  
ZhiWei Liu ◽  
Bin Yu ◽  
Bo Yu
Keyword(s):  
Modular Multiplication ◽  
Multiplication Algorithm ◽  
Montgomery Modular Multiplication

scholarly journals An improved wNAF scalar-multiplication algorithm with low computational complexity by using prime precomputation

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Huang Hai ◽  
Na Ning ◽  
Xing Lin ◽  
Liu Zhiwei ◽  
Yu Bin ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Scalar Multiplication ◽  
Low Computational Complexity ◽  
Multiplication Algorithm
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