Presentation slide of graduate course "Maths for Signal Processing and Communications"

1. EENGM0014 Mathematics for Signal Processing and
Communications
Tutorial 3
Soon Yau Cheong
University of Bristol
21 Oct 2016
Soon Yau Cheong (University of Bristol) EENGM0014 Mathematics for Signal Processing and Communications21 Oct 2016 1 / 3

2. Tutorial
1 TBD
Soon Yau Cheong (University of Bristol) EENGM0014 Mathematics for Signal Processing and Communications21 Oct 2016 2 / 3

3. LU Decomposition
Gaussian Elimination


a11 a12 a13
0 a22 a23
0 0 a33




x1
x2
x3

 =


b1
b2
b3


Soon Yau Cheong (University of Bristol) EENGM0014 Mathematics for Signal Processing and Communications21 Oct 2016 3 / 3

4. LU Decomposition
Gaussian Elimination


a11 a12 a13
0 a22 a23
0 0 a33




x1
x2
x3

 =


b1
b2
b3


LU Decomposition for square matrix A


a11 a23 a13
a21 a22 a23
a31 a32 a33

 =


l11 0 0
l21 l22 0
l31 l32 l33




u11 u12 u13
0 u22 u23
0 0 u33


Soon Yau Cheong (University of Bristol) EENGM0014 Mathematics for Signal Processing and Communications21 Oct 2016 3 / 3

5. LU Decomposition
Gaussian Elimination


a11 a12 a13
0 a22 a23
0 0 a33




x1
x2
x3

 =


b1
b2
b3


LU Decomposition for square matrix A


a11 a23 a13
a21 a22 a23
a31 a32 a33

 =


l11 0 0
l21 l22 0
l31 l32 l33




u11 u12 u13
0 u22 u23
0 0 u33


Solve Linear Equations
AX = B
(LU)X = B
Solve for Y , LY = B
ThenSolve for X, UX = YSoon Yau Cheong (University of Bristol) EENGM0014 Mathematics for Signal Processing and Communications21 Oct 2016 3 / 3