AD Tutorial at the TU Berlin

Univariate Taylor Propagation on Matrices (UTPM)
Application of Newton’s Method to defining equations
Defining equations of the QR decomposition:
0
0
0
D
= [Q] D [R] D − [A] D
D
= [Q] T D [Q] D − I
D
= P L ◦ [R] D ,
where (P L ) ij = δ i>j and element-wise multiplication ◦.
Defining equations of the symmetric eigenvalue decomposition
0
0
0
D
= [Q] T D [A] D[Q] D − [Λ] D
D
= [Q] T D [Q] D − I
D
= (P L + P R ) ◦ [Λ] D .
Defining equations of the Cholesky Decomposition
etc...
0
0
0
D
= [L] D [L] T D − [a] D
D
= P D ◦ [L] D − I
D
= P R ◦ [L] D .
Sebastian F. Walter, HU Berlin () Not So Short Tutorial OnAlgorithmic Differentiation Wednesday, 04.06.2010 25 / 39