NUMERICAL-ANALYSIS Course

Jacobi

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In the Jacobi method, the formula is based on two parts that you can evaluate first, and then at each iteration, you have to multiply your $X$ by the first part and add the second part.

\[ X^{(k+1)} \Leftrightarrow D^{-1} * (L + U) * X^{(k)} + D^{-1} * b \]

We got

  • PART1: $D^{-1} * (L + U)$
  • PART2: $D^{-1} * b$

Jacobi in R

# ...
##################################
# Complete here: add new variables
##################################
D.inv <- solve(D)
PART1 <- D.inv %*% (L + U)
PART2 <- D.inv %*% b 

repeat {
	# update our vector of values
	Xk <- PART1 %*% Xk + PART2
    # ...
}
# End: k= 22 
# The result is
# 3.999955 -1.000037 -1.000024