Optimal Estimation of Dynamic Systems, 2nd Edition

676 Optimal Estimation of Dynamic Systems

if a

kk

= 0

a

jk

← a

kj

/a

kk

, j = k + 1,...,n

a

jj

← a

jj

−a

jk

a

kj

, j = k + 1,...,n

end if

next k

where ← denotes replacement and ↔ denotes “interchange the value assigned to.”

The matrix U is given by the upper triangular part (including the diagonal elements)

of the overwritten A matrix, and the matrix L is given by the lower triangular part

(replacing the diagonal elements with ones) of the overwritten A matrix. More details

on Gaussian elimination can be found in Ref. [4].

LU and Cholesky Decompositions

The LU decomposition factors an n ×n matrix A into a product of a lower trian-

gular matrix L and an upper triangular ...