Algorithm 17.3 Givens QR Decomposition function GIVENSQR(A) % Computes the QR decomposition of A % Input: m× n matrix A % Output: m× n orthogonal matrix Q % and m× n upper triangular matrix R Q = I for i = 1:min(m-1,n) do for j = i+1:m do [c s] = givensparms(aii...
Since matrix equations with triangular matrices are easier to solve, the triangular matrices are very important in mathematics. For instance, the LU decomposition gives an algorithm to decompose any invertible matrix A into two triangular factors: a lower triangle matrix L and an upper triangle ...
A randomized stopping rule is an algorithm which observes the walk and stops it depending on the state passed and, perhaps, additional randomness. Denote by and τ the stopping state and stopping time of the randomized stopping rule. A a stopping time τ is called strong uniform if for all ...
Instead, as a measure of a matrix we will use its spectral radius. The proof of the inequality will use heavily special properties of upper-triangular matrices. It turns out that the applicability of our inequality is greatly enhanced by the fact that the spectral radius ρ(MN) of the ...
the uncertain aspect of determining the quantity of parameter values requiring adjustment adds complexity to the system. To address these challenges, the designed game incorporates the fuzzy module once again to craft a dynamic difficulty adjustment algorithm, intricately responsive to patient performance,...
Eqs. (2), (3) and (4) into Eq. (5), and a function ofα,β, andγcan be determined. As shown in Fig.6c and d, for the known world coordinate systemβ = 0°andγ = 90°. The value ofα = 88.82° was determined using the Trust-Region-Dogleg algorithm. ...
Hu, J., Huang, Y.Q., Shen, Q.: A high accuracy post-processing algorithm for the eigenvalues of elliptic operators. J. Sci. Comput. 52, 426–445 (2012) Article MATH MathSciNet Google Scholar Hu, J., Huang, Y.Q., Shen, Q.: Constructing both lower and upper bounds for the eig...
numericalalgorithm.Recently,thenumericalanalysis codeswithhighlyadvancedalgorithmshavebeen developedandthecomputationalperformanceshave been also progressed remarkablY, by which thermal-hydraulicevaluationsoflargeandcomplex regionshavebecomepracticablewithinreasonable ...
1.This article proposes a dynamic algorithm of Frequent Itemsets Mining based on Upper Triangular ItemSets Matrix(UTIM).频繁项集的生成是关联规则挖掘中的关键问题,提出了一种基于上三角项集矩阵的动态频繁项集挖掘算法。 6)upper triangular matrix ring上三角矩阵环 ...
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n×n upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for checking whether such an identity holds, in time polynomial in the le...