All Questions
7 questions
8
votes
2
answers
950
views
Best known bounds on (border) ranks of small matrix multiplication tensors?
The $(m,n,p)$-matrix multiplication tensor is a representation of the bilinear map $T\colon\mathbb{R}^{m\times n}\times\mathbb{R}^{n\times p}\rightarrow\mathbb{R}^{m\times p}$ given by $T(A,B)=AB$. ...
- 7,633
5
votes
0
answers
160
views
reference for perturbation of projection result
Let $A$ and $B$ have the same rank and dimensions. If $P_A$ denotes the projection onto the range space of $A$, then
$$
\|P_A - P_B\|_2 \leq \|A - B\| \cdot \min (\|A^\dagger\|_2, \|B^\dagger\|_2).
$$
...
- 922
4
votes
1
answer
408
views
Proof of Levinson-Durbin algorithm
Is there any article or reference book with a full proof of the Levinson-Durbin algorithm used for solving linear system with a Toeplitz matrix ?
- 41
4
votes
0
answers
136
views
What do we know about the generalized eigenvalue problem involving a projector?
Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$.
Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem
$$...
- 325
3
votes
1
answer
836
views
Solving multilinear equations
Let $N=\{1,2,\ldots,n\}$. Suppose we are given $n$ equations, with each equation taking the form $\sum_{A\subseteq N}\left(c_A \prod_{i\in A}x_i \right) = 0$, where each $c_A$ is a real number ...
- 239
3
votes
1
answer
175
views
Is there a classical textbook/reference on numerical discretization schemes?
I found that it is relatively easy to find a book that discusses Euler discretization or Runge-Kutta discretization, but I am not aware of one that is well-known and/or common knowledge (i.e., field-...
- 479
1
vote
0
answers
61
views
Discrete-to-continuum convergence of principal Fokker-Planck eigenvalues
I am looking for a reference justifying the following statement.
Let $L^n$ be any "reasonably consistent" finite-difference approximation of the Fokker-Planck operator in dimension $d=1$
$$
...
- 5,380