Question

in jacobi method the range of theta for getting least possible rotation is

Answer 1

The iterative process is terminated when a convergence criterion

Answer 2

Answer:

Getting theta the least possible rotation in the Jacobi method is when (p, q) or (q, p) entries are 0

Step-by-step explanation:

One of the major downsides of the symmetric QR algorithm is that it isn't parallelizable. Each orthogonal similarity metamorphosis that's demanded to reduce the original matrix A to slant form is dependent upon the former bone. In view of the elaboration of resemblant infrastructures, it is thus worthwhile to consider whether there are indispensable approaches to reducing an n × n symmetric matrix A to a slant form that can exploit these infrastructures.

we considered a rotational matrix. J(p, q,  θ

$\left[\begin{array}{ccc}1&0&0 \\o&c&s\\0&-s&c\end{array}\right]$

whereas in the row 2nd and 3rd there is p and q and similar in the column.

where c = cos θ and s = sin θ. When applied as a similarity metamorphosis to a symmetric matrix A, this matrix rotates rows and columns p and q of A through the angle θ so that the( p, q)  and( q, p) entries are zeroed. We call the matrix J( p, q, θ) a Jacobi rotation. It's actually identical to a Givens rotation, but in this context, we call it a Jacobi rotation to admit its innovator.

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