triangular decomposition

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1: 3.2 Linear Algebra

… ►If we denote by $𝐔$ the upper triangular matrix comprising the elements $u_{jk}$ in (3.2.3), then we have the factorization, or triangular decomposition, … ►We solve the system $𝐀𝛿𝐱=𝐫$ for $𝛿𝐱$, taking advantage of the existing triangular decomposition of $𝐀$ to obtain an improved solution $𝐱+𝛿𝐱$. …

2: 37.3 Triangular Region with Weight Function

§37.3 Triangular Region with Weight Function

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§37.3(i) Orthogonal Decomposition

►On the triangular region $\mathrm{△}$, see (37.2.17), define the weight function …which is normalized such that . … …

3: 37.14 Orthogonal Polynomials on the Simplex

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§37.14(i) Orthogonal Decomposition

… ►See §37.3 for the case $d=2$ (${\mathrm{△}}^2=\mathrm{△}$). …