(adsbygoogle = window.adsbygoogle || []).push({}); Question:

Ax=b

Let the coefficient matrix A be written in the form, where D is the diagonal matrix whose diagonal is the same as that of A, -L is the strictly lower triangular part of A and -U is the strictly upper part of A. Furthermore, letA=D-L-Ube the iteration matrix for Jacobi's method. Prove that Jacobi's method is convergent if the coefficient matrix is diagonally dominant.T_{j}= D^{-1}(L+U)

If A and b are given, I know how to use the Jacobi's method to find out whether or not A is convergent. But how should I prove that "Jacobi's method is convergent if A is diagonally dominant" using just those given letters and symbols?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How to prove a strictly diagonally dominant matrix is convergent

**Physics Forums | Science Articles, Homework Help, Discussion**