# Questions tagged [inverse-problems]

Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are often ill-posed. Not to be confused with the (inverse) tag.

301 questions
Filter by
Sorted by
Tagged with
91 views

### Sufficient conditions to guarantee that weakly convergent sequence also converges strongly

I know that any Hilbert space, $H$, satisfies the Radon-Riesz property: Any weakly convergent sequence, $x_n \rightharpoonup x$, such that $\lim_{n \rightarrow} \|x_n\| = \|x\|$, is also strongly ...
12 views

### First and second condition in Hadamard's Well-posedness

From, e.g., Wikipedia we have In mathematics, a well-posed problem is one for which the following properties hold: 1. The problem has a solution 2. The solution is unique 3. The solution's behavior ...
• 1
26 views

### Approximate a reaction-diffusion system by a "diffussion-then-reaction" system

Consider a 1D reaction-diffusion system with a scalar diffusion rate and a logistic reaction function: $$\frac{du}{dt} = D \nabla^2 u + \rho u(1-u).$$ Suppose the spatial domain is $\mathcal{X}=[0,10]$...
• 157
154 views

### If I can solve $Ax = b$ efficiently, is there a method to solve $(I+A)x=b$ efficiently?

Say if I already have the LU factorization of a square matrix $A$, is there an efficient way to get the LU factorization of $I+A$? (We may assume all the matrix I mentioned is invertible.) I know from ...
• 555
20 views

• 2,101
38 views

### find $D$ of $(D+A)$ for $diag((D+A)^-1)=k$

I am wondering whether it is possible to derive $D$ for $diag((D+A)^{-1})=k$ where $diag()$ produces a vector of diagonal elements of a squared matrix, $D$ is an unknown diagonal matrix with possible ...
• 141
42 views

### How can I find possible non-symmetric $A$ if $A^k$ is symmetric?

Assume $\bf A\in \mathbb R^{n\times n}$ If I know ${\bf A}^k$ and that it is symmetric, how can I systematically find the $\bf A$ which are not? Own work One approach I have considered is to assume a ...
• 26.1k
1 vote
169 views

• 451
28 views

• 183
109 views

### Finding the values of a matrix multiplied between two unknown matrices

This is a slightly vague question I think, but I am wondering if there is any elegant way of solving this problem. Say I have a multiplication between three unitary matrices operating on a vector, ...
• 25
1 vote
43 views

### Functional inverse problem based on a variational principle

I am trying to solve an inverse problem based on variational principle. I will first present a forward problem that is already solved, and then present the inverse problem that I am trying currently ...
82 views

### how to show inverse of M-by-N data matrix using singular value decomposition?

The question is from the exercise questions from the EE4595 course being taught in TUDelft. The question is as follows... So far my attempted solution is like the following. The discretised data ...
• 23
160 views

### Linear Algebra: Solving the minimization with vector p-norm.

The course this question is from is called Wavefield imaging, It gives the vector p-norm of an N-by-1 vector $x=[x_1,x_2,...,x_N]^T$ is defined as $$||x||_p=\left(\sum_{n=1}^N |x_n|^p \right)^{1/p}$$...
• 23
1 vote
I have the following problem: $$5\cos \theta_1+3\sqrt{3}\sin \theta_1=4\qquad\qquad\textbf{(I)}$$ $$5\sin \theta_1-3\sqrt{3}\cos \theta_1=6\qquad\qquad\textbf{(II)}$$ I have two seemingly correct ...