Reducing a formula containing Sum and matrices.












0












$begingroup$


M and T is a NxN Matrix, a and b are vectors with N length.
g(x) is a function that takes a vector and returns a vector with the same length.
g(x) inverse exists.
The vector multiplication: t = u*v is defined:
begin{align*}
t_{i} = u_{i}*v_{i}
end{align*}

The Number of matriaces used here is 2*o, I would like to reduce this for my algorithm,
both for speed and memory purposes. Is this possible?.
begin{align*}
f(a,b)=frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)(M_{k}g_{k}(b) + frac{T_{k}g_{k}(b)}{2})+
frac{M_{k}g_{k}(a)T_{k}g_{k}(b)}{2}+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o} =
frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)M_{k}g_{k}(b)+
M_{k}g_{k}(a)T_{k}g_{k}(b)+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o}
end{align*}

I am totally stuck at this, any help is appreciated!










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  • 1




    $begingroup$
    Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
    $endgroup$
    – Mason
    Dec 5 '18 at 4:21


















0












$begingroup$


M and T is a NxN Matrix, a and b are vectors with N length.
g(x) is a function that takes a vector and returns a vector with the same length.
g(x) inverse exists.
The vector multiplication: t = u*v is defined:
begin{align*}
t_{i} = u_{i}*v_{i}
end{align*}

The Number of matriaces used here is 2*o, I would like to reduce this for my algorithm,
both for speed and memory purposes. Is this possible?.
begin{align*}
f(a,b)=frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)(M_{k}g_{k}(b) + frac{T_{k}g_{k}(b)}{2})+
frac{M_{k}g_{k}(a)T_{k}g_{k}(b)}{2}+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o} =
frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)M_{k}g_{k}(b)+
M_{k}g_{k}(a)T_{k}g_{k}(b)+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o}
end{align*}

I am totally stuck at this, any help is appreciated!










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
    $endgroup$
    – Mason
    Dec 5 '18 at 4:21
















0












0








0


1



$begingroup$


M and T is a NxN Matrix, a and b are vectors with N length.
g(x) is a function that takes a vector and returns a vector with the same length.
g(x) inverse exists.
The vector multiplication: t = u*v is defined:
begin{align*}
t_{i} = u_{i}*v_{i}
end{align*}

The Number of matriaces used here is 2*o, I would like to reduce this for my algorithm,
both for speed and memory purposes. Is this possible?.
begin{align*}
f(a,b)=frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)(M_{k}g_{k}(b) + frac{T_{k}g_{k}(b)}{2})+
frac{M_{k}g_{k}(a)T_{k}g_{k}(b)}{2}+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o} =
frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)M_{k}g_{k}(b)+
M_{k}g_{k}(a)T_{k}g_{k}(b)+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o}
end{align*}

I am totally stuck at this, any help is appreciated!










share|cite|improve this question











$endgroup$




M and T is a NxN Matrix, a and b are vectors with N length.
g(x) is a function that takes a vector and returns a vector with the same length.
g(x) inverse exists.
The vector multiplication: t = u*v is defined:
begin{align*}
t_{i} = u_{i}*v_{i}
end{align*}

The Number of matriaces used here is 2*o, I would like to reduce this for my algorithm,
both for speed and memory purposes. Is this possible?.
begin{align*}
f(a,b)=frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)(M_{k}g_{k}(b) + frac{T_{k}g_{k}(b)}{2})+
frac{M_{k}g_{k}(a)T_{k}g_{k}(b)}{2}+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o} =
frac{(sum_{k=1}^o
g_{k}^{-1}(M_{k}g_{k}(a)M_{k}g_{k}(b)+
M_{k}g_{k}(a)T_{k}g_{k}(b)+
frac{T_{k}g_{k}(a)T_{k}g_{k}(b)}{3}))}{o}
end{align*}

I am totally stuck at this, any help is appreciated!







linear-algebra algorithms






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edited Dec 5 '18 at 5:00







Mikael Törnqvist

















asked Dec 5 '18 at 3:39









Mikael TörnqvistMikael Törnqvist

1011




1011








  • 1




    $begingroup$
    Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
    $endgroup$
    – Mason
    Dec 5 '18 at 4:21
















  • 1




    $begingroup$
    Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
    $endgroup$
    – Mason
    Dec 5 '18 at 4:21










1




1




$begingroup$
Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
$endgroup$
– Mason
Dec 5 '18 at 4:21






$begingroup$
Usually the expectation on this site is that you type out your mathematics rather than place an image. Atleast in part this will make your post more attractive to answer. Logistically, it's easier on the answerers to have the mathematics that s/he may need to include in the answer already typed out. Then we can just cut and paste the needed symbols rather than retype it.
$endgroup$
– Mason
Dec 5 '18 at 4:21












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