(a) Is the finite element matrix (11.171) diagonally dominant? (b) Does the Jacobi iteration scheme converge to...

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(a) Is the finite element matrix (11.171) diagonally dominant?
(b) Does the Jacobi iteration scheme converge to the solution to Me = b? How fast? Hint: Use Exercise 8.2.48.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 18, 2016 09:09 AM

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Repeat Prob. 11.8, but use Jacobi iteration.
Give a direct proof that the finite element matrix (11.171) is positive definite, by either (a) Determining its L D LT decomposition, or (b) Finding its eigenvalues, using Exercise 8.2.48.
Show that if A is strictly diagonally dominant, then ||Tj || < 1.
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(a) Is the finite element matrix (11.171) diagonally dominant? (b) Does the Jacobi iteration scheme converge to...

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a No b Yes The Jacobi iteration matrix T cf 1065 is the tridiagona...View the full answer

Applied Linear Algebra

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