# All Questions

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### Any literature that extensively discusses the ability to strongly interpolate computationally on little empirical data?

Any literature that extensively discusses the ability to strongly interpolate computationally on little empirical data? This topic has fascinated me, but I find that it seems a bit novel. Particulary, ...
16 views

### Instability at the boundary of a finite difference simulation of a hyperbolic PDE

I want to simulate the hyperbolic partial differential equation $$W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0,$$ but I am having trouble finding a discrete analog of this equation which is numerically ...
9 views

### DevMode, Videomodedescriptor: Screen Refresh Rate Data [closed]

The dmDisplayFrequency in DEVMODE appears to be the vertical {Wikipedia} refresh rate for the monitor- does that necessarily correspond to the ...
21 views

### Use BIConjugate Gradient with incomplete LU decomposition as preconditioner [closed]

see my question over here: https://stackoverflow.com/questions/69706672/use-biconjugate-gradient-with-incomplete-lu-decomposition-as-preconditioner What can I do to solve this problem?
34 views

64 views

### Numerical Partial Differentiation Check

In my computer vision course, we are working on extracting a 3D surface from a chain of 2D images taken under several conditions. This procedure is known as Photometric stereo. Prior to extracting the ...
84 views

### What is the best method to do a MC Integration of a multidimensional integral where the integration limits depend upon other variables?

What is the best method to do a Monte Carlo Integration of a multidimensional integral where the integration limits depend upon other variables? I am interested in getting a numerical value of a 5 ...
79 views

### Difference between asymptotic and non-asymptotic convergence in optimization?

I am reading some optimization methods and I am facing some issues with two terms "asymptotic and non-asymptotic convergence". What is the difference between them?
25 views

### How to identify the most different short sequence from a corpus that does not occur?

I would like to generate the most unique string (20 long, primer) of a defined length that does not occur in a much larger string (6.4 billion long, human genome). Of course, there could be many ...
56 views

### Good non oscilliatory derivatives for an exsisting grid

I'm calculating the entropy production of a shockwave by utilizing the equations: \begin{equation} \sigma = J'_q\frac{\partial}{\partial x}\left(\frac{1}{T}\right) +\frac{1}{T}\frac{4\eta}{3}\left(\...
80 views

### Implicit integrator for ODE with quadratic right-hand side

I have an ODE for an unknown $x(t):[0,\infty)\to\mathbb R^n$ of the following form: $$x_i'(t)=a_i^\top x(t) + x(t)^\top Q_i x(t),$$ for $i\in\{1,\ldots,n\}$. Here, the vectors $a_i\in\mathbb R^n$ ...
41 views

### Convergence of Fourier series on subinterval with data matching at discrete node set

I am numerical analyst, and want to prove a result I observe numerically. Let $f$ be a periodic function on $I = [-\pi,\,\pi]$ that is $q$ times continuously differentiable, with the $(q+1)$th ...
85 views

### PETSc-like library for Julia

I want to build an application for Material Point Method (and probably other meshfree methods too) in Julia and I am looking for library for direct and iterative solvers that can help me with it. One ...
70 views

### Is this a legit way to sample a random matrix spectrum?

In order to undergird a theoretical model concerning many body physics, I want to have exponentially large eigenvalue spectra from the random matrix GOE ensemble. its properties are mainly (i) a ...
I'm trying to solve $-u''=\cos(2 \pi x)$ with boundary conditions $u'(0)=u'(1)=0$ and the constraint $\int_{0}^1 u = 0$ I have to use linear finite elements, so let's assume that I have $M$ degrees of ...
I'm trying to understand the notion of relative error for vectors in $\mathbb{R}^n$, but it's not "clicking" somehow. \operatorname{\varepsilon-rel}(x_\text{approx}, x) = \frac{||x_\text{...