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NonlinearCholeskyFactorizationMIMO

Guides

  • Guide to ZigangPan`NonlinearCholeskyFactorizationMIMO`

Symbols

  • backsteppinglocaloptimalmatchingglobalinverseoptimalMIMO
  • linearFactorSequential
ZigangPan`NonlinearCholeskyFactorizationMIMO`
linearFactorSequential
​
{
f0
,
ftilde
} = linearFactorSequential[
f
,
xc
,
yc
] returns a formula
f0
and a formula
ftilde
of a tensor function
ftilde
[
xc
,
yc
] such that
f
=
f0
+
ftilde
.
yc
and
ftilde
〚
All
,...,All,1;;i〛 is a function of (
xc
,
yc
[[1;;i]]) only, i=1,...,
Length
[yc]. It assumes that
f
has a domain of definition that is includes in (
xc
,yci), where yci=
yc
except the last i indices are zeros.
f
: a formula for scalar, vector, matrix or tensor valued function with independent variables
Join
[
xc
,
yc
];
xc
: a vector of variables (maybe empty)
yc
: a vector of variables (must be nonempty)
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
f={x1+x2+x1*y2+y1^2*x2,x1-x2+y1^2+x1*x2*(y2+y2^2)};xc={x1,x2};yc={y1,y2};​​
linearFactorSequential
[f,xc,yc]
Out[1]=
{{x1+x2,x1-x2},{{x2y1,x1},{y1,x1x2(1+y2)}}}
In[2]:=
f={x1+x2+x1*y2+y1^2*x2,x1-x2+y1y2+x1*x2*(y2+y2^2)};xc={x1,x2};yc={y1,y2};​​linearFactorConvex[f,xc,yc]
Out[2]=
{x1+x2,x1-x2},{x2y1,x1},
y2
2
,x1x2+
y1
2
+x1x2y2
In[3]:=
f={x1+x2+x1*y2+y1^2*x2,x1-x2+y1y2+x1*x2*(y2+y2^2)};xc={x1,x2};yc={y1,y2};​​
linearFactorSequential
[f,xc,yc]
Out[3]=
{{x1+x2,x1-x2},{{x2y1,x1},{0,y1+x1x2(1+y2)}}}
SeeAlso
linearFactorConvex
RelatedGuides
▪
Guide to ZigangPan`NonlinearCholeskyFactorizationMIMO`
""

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