Suppose matrix $A$ is symmetric and positive definite. I'm studying the Weighted-Jacobi iteration method, but I don't know what value of weight $\omega$ I should pick. Most of the literature say that $\omega$ is usually chosen to be $\frac{2}{3}$. Why $\frac{2}{3}$, is there any proof on that?
2026-03-28 20:03:27.1774728207
Weighted-Jacobi method
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Look at https://www.google.com/url?sa=t&source=web&rct=j&url=https://ocw.mit.edu/courses/mathematics/18-086-mathematical-methods-for-engineers-ii-spring-2006/readings/am62.pdf&ved=2ahUKEwj9lduUoczhAhWBq54KHRaFDYgQFjABegQIBBAB&usg=AOvVaw172VJgpocqF3bOp7BEz8LP pages 4-5 have the explanation. Basically, it says that 2/3 is the optimal value for a system with a standard discrete Laplacian matrix