# Tagged Questions

Questions on numerical analysis/numerical methods; methods for approximately solving various problems that often do not admit exact solutions.

41 views

### DFT by $n$ samples of a continuous periodic signal with more than $n$ frequencies

It is known that if we only have $n$ samples and take DFT, we only get at most $n$ distinct frequency data. But let's say that there is a continuous periodic signal with more than $n$ frequencies, ...
39 views

### What is the condition of $\Delta t$ or $\Delta x$ in FEM

Recently, when I solved the convection-diffusion problem numerically, I found that it often showed NaN in my screen. :( The problem is: \begin{align} u_t + u_x - u_{xx} &= 0\\ u(x,0) &= u_0(x)...
21 views

### Consistent but not covergent

I have been asked to prove that the method: $$x_{n+3} + x_{n+2} - x_{n+1} - x_n = h\left(f_{n+3} + f_{n+2} + f_{n+1} + f_n\right)$$ is consistent, but not convergent. I have been able to show that ...
186 views

352 views

### the algorithm and computation cost for truncated SVD in rank k

It seems that the time cost of truncated SVD in rank k for matrix $A\in R^{m\times m}$ is $O(m^2 k)$. Could anyone show me some algorithms to calculate truncated SVD with the above time complexity?
66 views

### Stationary distribution of multidimensional birth-death process

I am considering a 2D birth-death process with a rate matrix $A$, with (1) state space: each dimension can take an integer value from $1$ to $V$ and there are two dimensions. Therefore the size of ...
222 views

67 views

48 views

### What is meaning of $FFT(\vec{E}(x,y ))$

What is the meaning and how one takes fourier transformation of vector that has spatial distrubution. Let say electric field (with transfer x, y distibution) with direction $$FFT(\vec{E}(x,y ))$$ ...
60 views

### Modified central difference formula

Prove or disprove the assertion: If $f$ is differentiable at $x$, then for $\alpha \neq 1$ $$\lim_{h \to 0} \frac{f(x+h)-f(x+ \alpha h)}{h- \alpha h} = f'(x)$$ I first ...
13 views

53 views

### Milstein scheme for stochastic differential equation with constant drift

The Milstein scheme to approximate the solution of an SDE is $$Y_{n+1} = Y_n + a\Delta_t + b\Delta W_t + \frac{1}{2} bb' ((\Delta W)^2 - \Delta)$$ where $\Delta_t$ is the time step size (usually ...
231 views

### Bisection method guessing interval

I know that generally the bisection method is used given a certain function and an interval where we know a root exists within it. What if we don't know the interval? Is there a way of "guessing" the ...
49 views

### Number of significant figures relative to true value of x

I've been stuck on this relatively simple matter for a while and I'd really appreciate some insight into what the actual answer should be. Say I'm given an approximate x value $x_A = 28.271$, and a ...
46 views

### Bernoulli monosplines

Please help me with Bernoulli monosplines. Let's consider $2\pi$-periodic cubic spline, which is consist from $N$ ranges $0<x_1<x_2<\cdots<x_N<2\pi$. We can introduce a periodic ...
103 views

### Space-Time FEM for parabolic problems

I am trying to solve a parabolic problem (an IBVP) in one spatial variable using the Galerkin method. After searching for inspiration, I find that the typical approach is to discretise the temporal ...
162 views