The minimum, maximum and average number of arithmetic operations both on polynomials and in the ground field are derived. We consider five different algorithms to compute gcd(A 1, A 2) where A 1, A 2∈ Z 2[ x] have degrees m≥n≥0. Compared with the classical Euclidean algorithm that...
Euclidean algorithm for Laurent polynomials Since R2021b collapse all in page Syntax dec = euclid(A,B) Description dec= euclid(A,B)returns an array of structures such that each row ofdeccorresponds to the Euclidean division of the Laurent polynomialAby the Laurent polynomialB: ...
Beckermann, B., and Labahn, G. "A fast and numerically stable Euclidean-like algorithm for detecting relatively prime numerical polynomials."Journal of Symbolic Computation. Vol.26, (1998): 691-714. Beckermann, B., and Labahn, G. "When are two numerical polynomials relatively prime?"Journal...
The QR algorithm is a numerical method of locating all eigenvalues of a real matrix. Section 6.4 ∎ The least-squares straight line is the line that minimizes the least-squares error for a given set of data. ∎ A vector x is the least-squares solution to Ax = b if and only if x...
valuation gcd algorithm for polynomials. Such a gcd algorithm is described in [98] for instance. In fact, there are two LSB divisions, the Plain LSB division and the Centered LSB division, according to the position of the quotient [non centered or centered]. There also exist two mixed group...
7 upper bounds for small \(\varepsilon \) (proof of theorem 4.1 ) in this section, we prove theorem 4.1 using an unfolding algorithm described in [ 18 ] and [ 22 ] based on melzak’s algorithm for finding the shortest steiner tree for a fixed steiner topology (if this ...
Thus, left cancellation of the factor s from all equations in (⁎) will give a right Euclidean algorithm for the original pair (a,b). (4) Let (a,b) be a Euclidean pair. Then (u−1au,u−1bu) is a Euclidean pair for every unit u∈R. More generally, if v,w are any ...
The cubic PHH-Bézier curve is then introduced and a new algorithm for their construction is proposed. According to geometric modeling, the error analysis between H-Bézier curve and PHH-Bézier curve is estimated. Finally, the proposed algorithm is verified experimentally. It is demonstrated that...
Let R[X] be theEuclidean ringof polynomials over the field of real numbers with the Euclidean function [phi](f) = deg(f) for each nonzero element f [member of] R[X]. Recall that for any nonzero element r in aEuclidean ringR with Euclidean function [phi], [phi]([1.sub.R]) [...
A new algorithm for human eye s wave-front aberration fitting withZernike polynomial; Zernike多项式拟合人眼波前像差的一种新算法 2. Regression analysis of wavefront fitting usingZernike polynomial; Zernike多项式波面拟合的回归分析方法 3. Analyzing thermal deformation of ultra-thin mirror usingZernike pol...