Reducing a formula containing Sum and matrices.
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
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
add a comment |
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
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
1
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.
– Mason
Dec 5 '18 at 4:21
add a comment |
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
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
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
linear-algebra algorithms
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
edited Dec 5 '18 at 5:00
Mikael Törnqvist
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
asked Dec 5 '18 at 3:39
Mikael TörnqvistMikael Törnqvist
1011
1011
1
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.
– Mason
Dec 5 '18 at 4:21
add a comment |
1
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.
– Mason
Dec 5 '18 at 4:21
1
1
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.
– Mason
Dec 5 '18 at 4:21
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.
– Mason
Dec 5 '18 at 4:21
add a comment |
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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.
– Mason
Dec 5 '18 at 4:21