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

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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
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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
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Data fitting 1 Data fitting 1 Often we want to fit data y values to a linear combination of nonlinear functions of x: f(x)= sum S C k f k (x) where the sum is over the fitting functions
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LEC07 - ELEC2102 - Lec 7 Matrices/ numerical methods...

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