Given a symmetric positive definite matrix A, the following algorithm computes the Cholesky factor H = hymh = Oi < J such that AHH.
Algorithm for k = 1 to n do
for i = 1 to k-1 do
end
ha
end
The above algorithm can be used to solve the symmetric positive definite system x as follows:
Step 1: Find the Cholesky factorization AHH
Step 2: Solve the lower triangular system for yHy = b
Step 3: Solve the lower triangular system for xH
(a) Using the above algorithm, compute the Cholesky factorization using Cholesky's algorithm of the matrix
1 - 2X
And find the range of values of A for which the factorization is valid. Given that X = 4 and b = 111, solve the system Ax = b.
(b) Find the block LU of A, where A = AB BA.
Use your factorization to solve Ax = b, where b = 4422.