Tagged Questions
1
vote
1answer
74 views
Floating point arithmetic
How can I prove that : a real number has a finite representation in the binary system if and only if it is of the form $$\pm \frac{m}{2^n}$$ where n and m are positive integers.
1
vote
3answers
297 views
Approximate a convolution as a sum of separable convolutions
I want to compute the discrete convolution of two 3D arrays: $A(i, j, k) \ast B(i, j, k)$
Is there a general way to decompose the array $A$ into a sum of a small number of separable arrays? That is:
...
0
votes
0answers
21 views
Elements of sparse matrix products
Following Problem:
I have to calculate a sum
$$
\sum_{k1,k2,k3,k4,k5} Mat1[k5,k1]*Mat2[k1,k2]*Mat3[k2,k3]*Mat4[k3,k4]*Mat5[k4,k5] * SomeFunction[k1,k2,k3,k4,k5]
$$
Mat1,..,Mat5 are large matrices ...
1
vote
0answers
69 views
Need little hint to prove a theorem .
I have an iterative method \begin{eqnarray}
X_{k+1}=(1+\beta)X_k-\beta X_k A X_k~~~~~~~~~~~~~~~~~ k = 0,1,\ldots
\end{eqnarray}
with initial approximation $X_0 = \beta A^*$ ($\beta$ is scalar ...
5
votes
1answer
185 views
Precision and performance of Euclidean distance
The usual formula for euclidean distance that everybody uses is
$$d(x,y):=\sqrt{\sum (x_i - y_i)^2}$$
Now as far as I know, the sum-of-squares usually come with some problems wrt. numerical ...
