Gauss-Seidel Algorithm

gausseidel.lua

-- Gauss Seidel Algorithm implemented through lua

function Norm(m)
	local n = 0
	for i,v in ipairs(m) do
	n = n + v^2
	end
	return math.sqrt(n)
end

local A = {
 {4,2,-4,0,2,4,0,0,0},
 {2,2,-1,-2,1,3,2,0,-6},
 {-4,-1,14,1,-8,-3,5,6,20},
 {0,-2,1,6,-1,-4,-3,3,23},
 {2,1,-8,-1,22,4,-10,-3,9},
 {4,3,-3,-4,4,11,1,-4,-22},
 {0,2,5,-3,-10,1,14,2,-15},
 {0,0,6,3,-3,-4,2,19,45}
}

local p,q,ACCURRACY=0,0,1E-4
local n = table.getn(A)
local MAX = 10000
local t = MAX
local x = {}
	for k = 1,n do x[k]=0 end


repeat
t=t-1
	q = Norm(x)
	for i=1,n do
	local lowSum = 0
		for j=1,i-1 do lowSum = lowSum+A[i][j]*x[j] end
		for j=i+1,n do lowSum = lowSum+A[i][j]*x[j] end
	x[i]=lowSum/A[i][i]
	end
	p = Norm(x)
until ((math.abs(p-q)<ACCURRACY) or (t==0))

for k,v in ipairs(x) do
print(k,v)
end