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Intelligent Numerical Computation 1
Numerical Analysis
MATLAB programming Numerical Methods Applications
Contents
Intelligent Numerical Computation 2
References:1. Numerical mathematics and computing, fourth Edition, Cheney&Kincaid, 19992. Lecture slides ftp://134.208.26.91 user:ndhu passwd:ndhu port:48103. G. Rechtenwald, Numerical methods with MATLAB: Implementation and application.
Intelligent Numerical Computation 3
A. Homework 30%
B. Midterm 30%
C Final Exam 40%
Grading
Intelligent Numerical Computation 4
Numerical Methods I
Locating roots Interpolation and numerical differentiation Numerical integration Solving a system of linear equations Approximation by spline functions Smoothing and the least-square method
Intelligent Numerical Computation 5
Locating roots of equations
Task:given a function f, find a solution x such that f(x)=0Related methods: Bisection method, Newton method, Secant method
0 1 2 3 4 5 6 7-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Intelligent Numerical Computation 6
Interpolation and numerical differentiation
Intelligent Numerical Computation 7
Interpolation and numerical differentiation
Intelligent Numerical Computation 8
Numerical integration:
Trapezoid rule, Simpson rule
system of linear equations
Ax=b
Approximation by spline functions:
natural cubic spline, B-splines
Intelligent Numerical Computation 9
Smoothing and the least square method
Intelligent Numerical Computation 10
Traveling salesman problems
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Independent component analysis
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
Observations
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Independent component analysis
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
0 20 40 60 80 100 120 140 160 180 200-2
0
2
Recovered sources
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Classification- Face detection
Intelligent Numerical Computation 14
Classification- Face detection
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Classification- Face detection
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Classification- Face recognition
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FNA細胞樣本
A camera on a Microscope
Feature extractor
Breast CancerDiagnosis
BenignOr Malignant
Features:clump thicknessuniformity of cell sizeuniformity of cell shapemarginal adhesionsingle epithelial cell sizebare nucleibland chromatinnormal nucleoli and mitoses
Classification – breast cancer diagnosis
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Blind source separation
music and speech
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Blind source separation
music and speech
Blind Source separation
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Blind source separation – fetal ECG
BSS
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sources
mixed images
AemICA
JadeICA
Figure 10
Intelligent Numerical Computation 22Figure 11
Fz
Cz
Pz
Oz
C3
F4
F3N1 N2
P3
P2
Intelligent Numerical Computation 23Figure 12
Fz
Cz
Pz
Oz
C3
F4
F3
N1 N2P2
P3
Intelligent Numerical Computation 24
x
x
x
xx
)(1,21 xG)(1,21 xG
)(1,21 xG
)(1,21 xG)(1,21 xG
Intelligent Numerical Computation 25
a.
b.
)(7 zy
))(exp())(exp( 2,212,21 zz GG
)(7 zy
)(7 zy
))(exp( 2,21 zG
))(exp( 2,21 zG
Intelligent Numerical Computation 26
)(zy
Function Approximation
Intelligent Numerical Computation 27
Basic structure of a flowchart or a program
start
end
statements
Statements are executed one by oneA statement can be an assignment: A = B*C-D : x = sort(x) a function for I/O : plot(x,y) : imread(X) a control statement -- if statement -- if else statement -- for statement -- while statement
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Control statements
If statement
condition
statements
false
true
tag = 0; if ~ tag tag = tag+1;end
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Control statements
If else statement
condition
statements
false or 0
true or 1
statements
if ~ tag tag = tag +1; else tag = tag –1; end
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Control statements
for statement
statements
false
true
Example x=2; for i = 1:10 x = x*x; end
i =1
10i
i=i+1
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Control statements
while statement
statements
false
true
Example
a=1; b=2; while a < 100 a = a*b; end
a<100
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Input your data, including texts, images, and sounds Output: 2D plots & output messages Basic control: if, for, while statements Matrix manipulations Function call Speeding-up programs Coding a method Solving a problem
MATLAB Programming
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