Square Root Method

The square root method is an algorithm which solves the matrix equation

(1)

for , with a symmetric matrix and a given vector. Convert to a triangular matrix such that

(2)

where is the transpose. Then

			(3)
			(4)

so

(5)

giving the equations

			(6)
			(7)
			(8)
			(9)
			(10)

These give

			(11)
			(12)
			(13)
			(14)
			(15)

giving from . Now solve for in terms of the s and ,

			(16)
			(17)
			(18)

which gives

			(19)
			(20)
			(21)

Finally, find from the s and ,

			(22)
			(23)
			(24)

giving the desired solution,

			(25)
			(26)
			(27)