Y-W

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AcronymDefinition
Y-WYule-Walker equation
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An order recursive algorithm is proposed to solve 2D Yule-Walker equations. Modeling of 2D AR processes with various regions of support is considered in [10].
which are obtained from the Yule-Walker equations. From Table 3, [r.sub.1] = -0.39 and [r.sub.2] = 0.30.
In what follows, an important role is played by the so-called Yule-Walker equations. For an n x n symmetric Toeplitz matrix [T.sub.n], defined by (1,[t.sub.1],[t.sub.2],...,[t.sub.n-1]),this system of linear equations is given by [T.sub.n][y.sup.(n)]=-t where t=[([t.sub.1], ..., [t.sub.n]).sup.T].
In what follows, an important role is played by the so-called Yule-Walker equations. For an n x n symmetric Toeplitz matrix [T.sub.n], defined by (l,[t.sub.1],[t.sub.2], ..., [t.sub.n-1]), this system of linear equations is given by [T.sub.n][y.sup.
In what follows, an important role is played by the so-called Yule-Walker equations. For an n x n symmetric Toeplitz matrix [T.sub.n], defined by (1, [t.sub.1], ..., [t.sub.n-1]), this system of linear equations is given by [T.sub.n][y.sup.n]=-t where t=[([t.sub.1], ..., [t.sub.n]).sup.T].
Partial autocorrelation coefficients ck, could be calculate through the Yule-Walker equations, which put about autocorrelation coefficients, previously calculated, with partial autocorrelation coefficients that has to be determined.
To compute the Newton step in (Mackens & Voss, 2000; Mastronardi & Boley, 1999), these methods use a recursion for the evaluation of the characteristic polynomial and its derivative which requires O([n.sup.2]) flops to solving the Yule-Walker equations. Melman in (Melman,2006) show that this recursion can be replaced by a shorter computation, involving the computation of the trace of an appropriate matrix, and, after solving the Yule-Walker equations, requiring only O(n) flops.