{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# LEC07 - ELEC2102 Lec 7 Matrices numerical methods...

This preview shows pages 1–4. Sign up to view the full content.

ELEC2102 ELEC2102 - Lec Lec 7 Matrices/ numerical methods introduction Text 3.2, 6.1-6.3 LU Matrix LU Matrix decomposition decomposition L and U matrices are easy to invert P swaps rows P . M = L . U

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
LU decomposition 2 LU decomposition 2 P rearranges rows to minimise numerical error For a set of equations M . x = y L . U . x = P . y or L . z = P . y where z = U . x solve z = L \ P . y then x = U \ z Matlab uses this method with x = M \ y but also some other methods depending on M and y QR Matrix decomposition QR Matrix decomposition M = Q . R R is upper triangular and Q is a square orthonormal matrix: Different columns have an inner product of zero and the inner product of a column with itself is one col(n) T x col(m)=0 (m not equal to n) col(n) T x col(n)=1 Q T x Q = I Note: col() is not a Matlab command use “:” to do this Use QR for data fitting – see later