Tagged Questions
1
vote
1answer
52 views
How to find the unknown values in this Numerical Integration type?
Given the following type of numerical integration:
$$I(f)=\int_0^1 f(x) \, dx \approx \frac 12 f(x_{0}) +c_1 f(x_1) $$
a) Find the values of: the coefficient $c_1$ and points $x_0$ and $x_1$ so ...
2
votes
1answer
94 views
Relation between positive definite Hermitian matrices with their inverses
Let $A$ and $B$ be two positive definite Hermitian matrices. Show that the Hermitian matrix $$C\ =\ A^{-1} + B^{-1} - 4(A + B)^{-1}$$ is also positive definite.
Thanks in advance.
1
vote
0answers
37 views
Eigenvalues of discretized linear integral operator
Suppose I have the following kernel operator:
$Af(x) = \int_{-1}^1 K(x-y)f(y)dy$
which is also positive and compact. Hence, it has a countable set of positive eigenvalues. Suppose those eigenvalues ...
2
votes
1answer
69 views
Matrix inversion of an analytical function
Following problem:
I have a function
$f(x_1,x_2)$
and Im looking for the inverse $finv(x_1,x_2)$ of the function which is defined through:
$\int f(x_1,y)\cdot finv(y,x_2) d y =\delta(x_1,x_2) $
...
