Post on 12-Sep-2015
description
pi pi ( 343)
pi pi : 9 2012
7 2012
: pi pi , pipipi . pi !
pi pi. pi pi pi pi pi. pi pipi pi. pi pi , pi ( pi, pi, , .pi.) ( pi pi - - pi pi ) pi, pi pi. pi , pi, pi pi pi1 , pi pi . pi pi pi.: pi pi pi pi pi - pi pi . pi pi . pi- pi ( pi) pi .
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1. fj pi, pi pi pi pi pi Mj . pi pi pi pi pi pi pipi pi pipi pi.
f1(x) = x lnx, x > 0 f2(x) =
1xp , p Z+, x 1 f3(x1, x2) =
x21 + x
22 ( pi pi 2
pi pi.) f4(x) =
1 + x 1 pi x (1,).
2. pipi2 x ... pi f(x) fprog(x) pi pi 1, 2, 3 pi ( ), . , pi u. xprog = x(1 + ) f(xprog) = fprog(x). pipi x, 1, 2, 3 pi (. pi pi u, pi pi 12, 21 .pi.). pi pi , || u x
1 pi .2 W. Gautschi
1
. pi x (1,) pi u ... IEEE . , ( pi, pi ) pipi , pi , pi pi f . pi.
3. pi MATLAB; pi .
[0/(1 == 1 + eps4) ; 0/(1 == (1+eps)*(1/(1+eps))) ; ...inf*((1+eps/4)-1) ; realmax + 1 = realmax]
2
pi pi pi pi pi pi Maclaurin
cosx0 = 1 x20
2!+x404! . . . =
+n=0
(1)n x2n0
(2n)!
sinx0 = x0 x30
3!+x505! . . . =
+n=0
(1)n x2n+10
(2n+ 1)!
1. pi MATLAB powersin powercos pipi- pi . pi pi . s t -pi , pipi s + t == s. pi pi ; pi pi . (: pi (Moler, Matlab .69).
2. x0 pi2 , pi,3pi2 , 2pi,
11pi2 ,
(21+)pi2
(21+)pi4 pi
= 10 + , pi . pi ; . pi ; ( MATLAB).
3. pi x0 pi . pi pi pipi .
4. x0 = pi30 . pi pi pi . ns pi pi pi pi powersin nc pi pi pi pi powercos. pi pi pi pi pi .
5. powersin pi k , ns = 2(k 1) + 1, ns x0 pi pi pi . powercos nc = 2(k 1). - Vandermonde Vc R(nc+1)(nc+1) Vs R(ns+1)(ns+1)
2
vander pi pi MATLAB c
s pi3
c
=
1 + 1101 + 2101 + 310
...1 + nc10
1 + 1+nc10
s
=
1 + 1101 + 2101 + 310
...1 + ns10
1 + 1+ns10
pi cond MATLAB pi Vc Vs. pi yc = cos(c) ys = sin(s) pi Vchc = yc Vshs = ys \ MATLAB. pi ;
c
=
234...
1 + nc2 + nc
s =
234...
1 + ns2 + ns
pi Vc Vs pi pipi pi ;
3
pi pi pi ( pi, pi -) pi pi pipi ...
pi
pn(x) = x(x 1)n3(x 2)(x 3).
n = 4, 6, 9, 12, 15 pn poly pi roots. pi pi pi ; , ; pn(x) pi roots pi plot(, x pi y .) pi pn(x) ( ) pi .: pi pi pi n, pi subplot pi n pi ( s pi, ).
pi pi e-mail sci_2012_hw02_xxxx .rar sci_2012_hw02_xxxx.rar.
3 Taylor pi pi pi 1, x, x2, . . ..
3