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NonlinearCholeskyFactorization

Guides

  • Guide to ZigangPan`NonlinearCholeskyFactorization`

Symbols

  • approximateHJIequation
  • approximatenonlinearCholeskyfactorization
  • backsteppinglocaloptimalmatchingglobalinverseoptimal
  • backsteppinglocaloptimalmatchingglobalinverseoptimalNew
  • backsteppinglocaloptimalmatchingglobalinverseoptimalN
  • backsteppinglocaloptimalmatchingglobalinverseoptimalNNew
  • expandseriesntruncate
  • monomialsofgivenorder
ZigangPan`NonlinearCholeskyFactorization`
expandseriesntruncate
​
{fa,faca}=expandseriesntruncate[f,xc,m]
expands a formula
f
, whose independent variables are listed in the vector
xc
, into its Taylor series in all of the variables up to
m
-th order. The returned variables are
fa
= the truncated Taylor series in formula.
faca
= the coefficients array of fa in terms of
xc
.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
xc={x1,x2}
Out[1]=
{x1,x2}
In[2]:=
assumptions=((x1|x2)∈Reals)
Out[2]=
(x1|x2)∈
In[3]:=
fe[x1_,x2_]:={x2+x1^2,0}
In[4]:=
expandseriesntruncate
[1+x,{x,y},10]
Out[4]=
{1+x,{1,{1,0}}}
In[5]:=
expandseriesntruncate
[Apply[fe,xc],xc,10]
Out[5]=
{{
2
x1
+x2,0},{{0,0},{{0,1},{0,0}},{{{1,0},{0,0}},{{0,0},{0,0}}}}}
In[6]:=
expandseriesntruncate
[Exp[x],{x},10]
Out[6]=
1+x+
2
x
2
+
3
x
6
+
4
x
24
+
5
x
120
+
6
x
720
+
7
x
5040
+
8
x
40320
+
9
x
362880
+
10
x
3628800
,1,{1},
1
2
,
1
6
,
1
24
,
1
120
,
1
720
,
1
5040
,
1
40320
,
1
362880
,
1
3628800

SeeAlso
monomialsofgivenorder
 
▪
approximateHJIequation
 
▪
approximatenonlinearCholeskyfactorization
""

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