Tagged Questions

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.
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: ...
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 ...
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 ...
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 ...
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