Results 251 to 260 of about 203,139 (278)

The Minimal Euclidean Norm of an Algebraic Number Is Effectively Computable

Journal of Algorithms, 1994
For a polynomial \(P(x)= p_ 0+\dots +p_ n x^ n\), the Euclidean norm \(\| P\|\), defined to be the Euclidean norm of the vector \((p_ 0,\dots, p_ n)\). The minimal Euclidean norm \(\| \alpha\|_{\min}\) of an algebraic number \(\alpha\) is defined to be the minimum of \(\| P\|\) over all polynomials with integer coefficients for which \(P(\alpha)=0 ...
Michael Filaseta, M. L. Robinson, Ferrell S. Wheeler   +2 more
openaire   +1 more source

NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE

International Journal of Number Theory, 2012
Let K be a cyclic number field of prime degree ℓ. Heilbronn showed that for a given ℓ there are only finitely many such fields that are norm-Euclidean. In the case of ℓ = 2 all such norm-Euclidean fields have been identified, but for ℓ ≠ 2, little else is known. We give the first upper bounds on the discriminants of such fields when ℓ > 2.
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A VLSI algorithm for computing the Euclidean norm of a 3D vector

IEEE Transactions on Computers, 2000
A digit-recurrence algorithm for computing the Euclidean norm of a three-dimensional (3D) vector which often appears in 3D computer graphics is proposed. One of the three squarings required for the usual computation is removed and the other two squarings, as well as the two additions, are overlapped with the square rooting.
Naofumi Takagi, Seiji Kuwahara
openaire   +1 more source

A quadratically convergent method for minimizing a sum of euclidean norms

Mathematical Programming, 1983
The author considers the problem of minimizing a sum of Euclidean norms \[ F(x)=\sum^{m}_{i=1}r_i(x) \] where the residuals \(r_i(x)\) are affine functions from \(R^n\) to \(R^l\) (\(n\geq l\geq 2,\quad m\geq 2)\). This arises in a number of applications, including single- and multi-facility location problems.
openaire   +1 more source

Quaternionic Generalized Norm Retrieval in Quaternion Euclidean Spaces

Advances in Applied Clifford Algebras
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Yang, Ming, Li, Yun-Zhang
openaire   +1 more source

A Rapid Euclidean Norm Calculation Algorithm that Reduces Overflow and Underflow

Lecture Notes in Computer Science, 2021
Shuhei Kudo, Daichi Mukunoki, Toshiyuki Imamura   +2 more
exaly  

The Kronecker-Vahlen theorem fails in real quadratic norm-Euclidean fields

Journal of Symbolic Computation, 2021
Maksim Vaskouski
exaly  

Normativity of the Euclidean Ideal

2021
openaire   +1 more source

On Euclidean norm approximations

Pattern Recognition, 2011
M Emre Celebi, Fatih Celiker
exaly  

A quasi-Euclidean norm to speed up vector median filtering

IEEE Transactions on Image Processing, 2000
M Barni, F Bartolini, V cappellini
exaly