.lst-kix_ohzxsp1deq34-0 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-0,decimal) ". "}.lst-kix_ohzxsp1deq34-3 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-3,decimal) ". "}ol.lst-kix_ohzxsp1deq34-8.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-8 0}ol.lst-kix_ohzxsp1deq34-5.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-5 0}ol.lst-kix_h70xyuvb0pq7-0.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-0 0}.lst-kix_ohzxsp1deq34-2 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-2,lower-roman) ". "}.lst-kix_ohzxsp1deq34-1 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-1,lower-latin) ". "}.lst-kix_ohzxsp1deq34-7 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-7}ol.lst-kix_3vyyr53pt88i-6.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-6 0}.lst-kix_ohzxsp1deq34-7 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-7,lower-latin) ". "}.lst-kix_h70xyuvb0pq7-4 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-4}.lst-kix_ohzxsp1deq34-6 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-6,decimal) ". "}.lst-kix_ohzxsp1deq34-8 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-8,lower-roman) ". "}ol.lst-kix_h70xyuvb0pq7-6.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-6 0}ol.lst-kix_3vyyr53pt88i-3.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-3 0}.lst-kix_ohzxsp1deq34-4 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-4,lower-latin) ". "}.lst-kix_ohzxsp1deq34-8 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-8}ol.lst-kix_3vyyr53pt88i-0.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-0 0}ol.lst-kix_h70xyuvb0pq7-3.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-3 0}.lst-kix_ohzxsp1deq34-5 > li:before{content:"" counter(lst-ctn-kix_ohzxsp1deq34-5,lower-roman) ". "}ol.lst-kix_ohzxsp1deq34-2.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-2 0}.lst-kix_6atpr0wc9bjy-6 > li:before{content:"- "}.lst-kix_6atpr0wc9bjy-5 > li:before{content:"- "}.lst-kix_6atpr0wc9bjy-4 > li:before{content:"- "}.lst-kix_6atpr0wc9bjy-3 > li:before{content:"- "}.lst-kix_6atpr0wc9bjy-0 > li:before{content:"- "}.lst-kix_h70xyuvb0pq7-3 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-3}.lst-kix_6atpr0wc9bjy-2 > li:before{content:"- "}.lst-kix_6atpr0wc9bjy-1 > li:before{content:"- "}.lst-kix_ohzxsp1deq34-5 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-5}ol.lst-kix_h70xyuvb0pq7-5.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-5 0}ol.lst-kix_ohzxsp1deq34-0.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-0 0}.lst-kix_h70xyuvb0pq7-8 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-8,lower-roman) ". "}.lst-kix_h70xyuvb0pq7-1 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-1}ol.lst-kix_ohzxsp1deq34-7.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-7 0}.lst-kix_ohzxsp1deq34-4 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-4}.lst-kix_h70xyuvb0pq7-7 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-7,lower-latin) ". "}ol.lst-kix_3vyyr53pt88i-5.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-5 0}.lst-kix_h70xyuvb0pq7-4 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-4,lower-latin) ". "}.lst-kix_h70xyuvb0pq7-5 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-5,lower-roman) ". "}.lst-kix_h70xyuvb0pq7-6 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-6,decimal) ". "}.lst-kix_3vyyr53pt88i-2 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-2}.lst-kix_h70xyuvb0pq7-0 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-0,decimal) ". "}.lst-kix_h70xyuvb0pq7-1 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-1,lower-latin) ". "}.lst-kix_3vyyr53pt88i-5 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-5}.lst-kix_3vyyr53pt88i-8 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-8}ul.lst-kix_6atpr0wc9bjy-8{list-style-type:none}.lst-kix_h70xyuvb0pq7-3 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-3,decimal) ". "}ol.lst-kix_ohzxsp1deq34-0{list-style-type:none}.lst-kix_h70xyuvb0pq7-2 > li:before{content:"" counter(lst-ctn-kix_h70xyuvb0pq7-2,lower-roman) ". "}ol.lst-kix_ohzxsp1deq34-2{list-style-type:none}ol.lst-kix_ohzxsp1deq34-1{list-style-type:none}ol.lst-kix_ohzxsp1deq34-4{list-style-type:none}ol.lst-kix_ohzxsp1deq34-3{list-style-type:none}ol.lst-kix_ohzxsp1deq34-6{list-style-type:none}ol.lst-kix_ohzxsp1deq34-6.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-6 0}ol.lst-kix_ohzxsp1deq34-5{list-style-type:none}.lst-kix_h70xyuvb0pq7-7 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-7}ol.lst-kix_ohzxsp1deq34-8{list-style-type:none}ol.lst-kix_ohzxsp1deq34-7{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-4{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-5{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-6{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-7{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-0{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-1{list-style-type:none}ol.lst-kix_3vyyr53pt88i-4.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-4 0}ul.lst-kix_6atpr0wc9bjy-2{list-style-type:none}ul.lst-kix_6atpr0wc9bjy-3{list-style-type:none}.lst-kix_ohzxsp1deq34-2 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-2}.lst-kix_3vyyr53pt88i-3 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-3}ol.lst-kix_h70xyuvb0pq7-1{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-0{list-style-type:none}.lst-kix_ohzxsp1deq34-1 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-1}.lst-kix_3vyyr53pt88i-4 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-4}.lst-kix_h70xyuvb0pq7-8 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-8}ol.lst-kix_3vyyr53pt88i-8{list-style-type:none}ol.lst-kix_3vyyr53pt88i-7{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-4.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-4 0}ol.lst-kix_3vyyr53pt88i-0{list-style-type:none}ol.lst-kix_3vyyr53pt88i-2{list-style-type:none}ol.lst-kix_3vyyr53pt88i-1{list-style-type:none}ol.lst-kix_3vyyr53pt88i-2.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-2 0}ol.lst-kix_3vyyr53pt88i-4{list-style-type:none}ol.lst-kix_3vyyr53pt88i-3{list-style-type:none}ol.lst-kix_ohzxsp1deq34-4.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-4 0}ol.lst-kix_3vyyr53pt88i-6{list-style-type:none}ol.lst-kix_3vyyr53pt88i-5{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-5{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-4{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-3{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-2{list-style-type:none}ol.lst-kix_ohzxsp1deq34-1.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-1 0}ol.lst-kix_h70xyuvb0pq7-8{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-7{list-style-type:none}ol.lst-kix_h70xyuvb0pq7-6{list-style-type:none}.lst-kix_h70xyuvb0pq7-0 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-0}ol.lst-kix_h70xyuvb0pq7-7.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-7 0}ol.lst-kix_3vyyr53pt88i-1.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-1 0}ol.lst-kix_ohzxsp1deq34-3.start{counter-reset:lst-ctn-kix_ohzxsp1deq34-3 0}.lst-kix_h70xyuvb0pq7-6 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-6}.lst-kix_3vyyr53pt88i-6 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-6}.lst-kix_3vyyr53pt88i-1 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-1}.lst-kix_3vyyr53pt88i-7 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-7}ol.lst-kix_h70xyuvb0pq7-1.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-1 0}.lst-kix_6atpr0wc9bjy-7 > li:before{content:"- "}.lst-kix_3vyyr53pt88i-0 > li{counter-increment:lst-ctn-kix_3vyyr53pt88i-0}ol.lst-kix_h70xyuvb0pq7-8.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-8 0}.lst-kix_6atpr0wc9bjy-8 > li:before{content:"- "}.lst-kix_h70xyuvb0pq7-5 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-5}ol.lst-kix_3vyyr53pt88i-8.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-8 0}.lst-kix_3vyyr53pt88i-1 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-1,lower-latin) ". "}.lst-kix_3vyyr53pt88i-2 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-2,lower-roman) ". "}.lst-kix_ohzxsp1deq34-6 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-6}.lst-kix_ohzxsp1deq34-0 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-0}.lst-kix_h70xyuvb0pq7-2 > li{counter-increment:lst-ctn-kix_h70xyuvb0pq7-2}.lst-kix_3vyyr53pt88i-3 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-3,decimal) ". "}ol.lst-kix_3vyyr53pt88i-7.start{counter-reset:lst-ctn-kix_3vyyr53pt88i-7 0}.lst-kix_3vyyr53pt88i-0 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-0,decimal) ". "}.lst-kix_3vyyr53pt88i-8 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-8,lower-roman) ". "}ol.lst-kix_h70xyuvb0pq7-2.start{counter-reset:lst-ctn-kix_h70xyuvb0pq7-2 0}.lst-kix_3vyyr53pt88i-7 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-7,lower-latin) ". "}.lst-kix_3vyyr53pt88i-5 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-5,lower-roman) ". "}.lst-kix_3vyyr53pt88i-6 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-6,decimal) ". "}.lst-kix_3vyyr53pt88i-4 > li:before{content:"" counter(lst-ctn-kix_3vyyr53pt88i-4,lower-latin) ". "}.lst-kix_ohzxsp1deq34-3 > li{counter-increment:lst-ctn-kix_ohzxsp1deq34-3}
3/29/2016Don't forget about the age old question of How can you determine relationships between two variables?
Head start on Project 2
Matlab:
F = at x 1 / (1 + 4*x^ 2)j
N = 10j i = [0:n]j
We also discuss several other topics like What is an organizational cognition?
% equally spaced points
X = -1 + 2* i / nj y = f(x)j nx = length(x)
The basic interpolation is: Lagrange
x
X0 x1 x2
y
Y0 y1 y2
Basic: P(x1) = y1 = f(x1)We also discuss several other topics like Describe the characteristics of a moon jellyfish?
If you want to learn more check out What are unattainable and therefore discouraging to most employees?
Hermite: P(x) = y1 = f(xi) - this will be a higher degree
The hard part is coding the lagrange polynomialsIf you want to learn more check out What were the consequences of a single global economy?
P(a) = 
yi Li(a) li(a) = 
If you want to learn more check out synaptic knob
% Graphing points
Xx = [-1: 0.01:1]; nxx = length(xx)j
For k = 1:nxx
A = xx (k);
%Good(k) = P(a) = P(xx(k))
Pa = 0;
For i = 1:nx
Ax = a-x;
J = [1:i - 1, i + 1:nx];
Li = prod(ax(j)./(x(i) - x(j)))
Pa = Pa + y(i)*Li
end(k) = Pa;
plot(x,y,’*’,xx,f(xx),’r’,xx,pp,’b’)
Note:
A = (x0)then ax = a - x = (a - x0) vector in Matlab
(x1) (a - x1)
(...) (,... )
- This is showing that we assume out function approximation will always get better as we increase the degree, but that’s not the case
Part 2 is the same code, but you use Chebyshev nodes (but the part (III) of both of these part 1 and 2 are different
% Chebyshev Nodes
X = cos((2*i + 1)*Pi)/(2*n + 2))i
Note: for n = 10, the function and polynomial look to be about the same
**the way the points are spaced makes a huge difference
For Chebyshev nodes, increasing the n values actually does improve the approximation polynomial
Up to a certain point / number of n then it will diverge from the function
**There may be something wrong with his code, or it’s just the error when you enter n = 1000 for Chebyshev nodes
Most likely it is the error because the polynomial
Error is shown below and it is fine at n = 500
norm(f(x).PP(x))
Example of Hermite Polynomial in book
x
x0
...
xn
y
C10
...
Cn0
y1
C11
...
Cn1
P(x) =C10Ai(x) + Ci1Bi(x)
Ai(xj) = Fis Fis = 1 if i = j
A1(xj) = 0 0 if i
j
B1(xj) = 0
Bj(xj) = 0
**Note: you do not have to use this form, you can look Lpn easier one online
Ai(x) = [1 - 2(x - xi)li1(xi)li2(x)
Bi(x) = (x - xi)li2(x)
How do we get li1(x). Take the derivative of li(x)
Example:
l0(x) = 
(x) = 
[(x - x1) + (x - x2)
X
Y
y1
X0
Y0
yi
X1
Y1
yi
X2
Y2
y2i
3/31/2016
Hermite Polynomial in Matlab
P(x) = yiAi(x) + yi1Bi(x) li(x) = 
