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14 votes
1 answer
2k views

On the non-rigorous calculations of the trajectories in the moon landings

In a paragraph written by a person emphasizing that rigour is not everything in mathematics (I wish I had written down the details), it was stated that the moon landings would have been impossible ...
teil's user avatar
  • 4,351
7 votes
4 answers
1k views

Reasonable "Random" matrices to test numerical algorithms

Hello, in numerical analysis, it is common to compare the behavior of different algorithms, and of different implementation of algorithms. This occurs not only on the theoretical level, but also on ...
shuhalo's user avatar
  • 5,327
5 votes
1 answer
213 views

Numerical instability of the axis-angle representation of rotations in 3D

Suppose that I have $1000$ pair of points where each pair consists of a point in $\mathbb{R}^3$ and its image after a rotation in $\mathrm{SO}(3)$ with some noise. I have used RANSAC to find the ...
stressed out's user avatar
3 votes
1 answer
187 views

Variation of steepest descent/Laplace methods for non-exponential integrands

I was wondering if versions of the Laplace/steepest descent methods exists for integrals of the type $$\int_C f(z) M(\lambda g(z)) dz$$ for $\lambda >>0$ functions $f(z), g(z): \mathbb C \...
Mr_3_7's user avatar
  • 135
2 votes
1 answer
421 views

Is it possible to obtain orthogonal (but not normalized) vectors after QR factorization?

After QR decomposition of a matrix, $M$, the columns of Q are orthonormal. Is it possible after obtaining Q, we recover unnormalized column vectors from $Q$? For example, the matrix M has the ...
ACR's user avatar
  • 879
2 votes
1 answer
81 views

IVP accuracy - scheme accuracy Vs. derivative accuracy?

General Question: If I have an IVP with periodic and continuous initial condition, which rules the accuracy of the scheme - the manner in which we approximate spatial derivative or the acuuracy of the ...
Amir Sagiv's user avatar
  • 3,574
1 vote
0 answers
144 views

Recursive formula for integral of Chebyshev-type integral

Define $$ I_{m,n}(x,y,r) = \int_a^b T_m(x + r \sin(\gamma)) T_n(y-r \cos(\gamma)) d\gamma $$ where $T_m(x)$ are the Chebyshev polynomials of the first kind, and $a$ and $b$ are constants. Assume that ...
Oren B.'s user avatar
  • 11
1 vote
0 answers
259 views

Industrial research projects on "mathematical modeling and PDEs" [closed]

Apparently there are several companies in a great variety of fields (medical, biological, engineering, etc.) that need "consulting on mathematical modeling and PDEs" from applied mathematicians. I'...
user avatar
0 votes
1 answer
114 views

Fit a system of linear ODEs from several experiments

Assume we are given several initial vectors $x^{(1)},\ldots,x^{(r)} \in \mathbb{R}^n$, where the dimension $n=6$ (in any event a number below 10) , and the number of initial vectors $r$ is in the ...
tobias's user avatar
  • 749
0 votes
1 answer
207 views

Regular Perturbation Series soln to eqn

I want to find the a 3 term perturbation soln of (i) $(1+x)^3 = ex$ where $e\ll1$ Direct substitution of the regular perturbation series $x = x_0 + ex_1 + e^2x_2$ into (i) does not work I ...
Matt Brenneman's user avatar
0 votes
0 answers
98 views

Interpolation polynomials with constraints

Lets consider a collection of $n$ points $\{Z_i\}_{i=1}^n\subseteq \mathbb{D}^k(1)=\{(z_1,\ldots,z_k)\in\mathbb{C}^k:\forall j\leq k, |z_j|\leq 1\}$. Let $h: \{Z_i\}_{i=1}^n \to \mathbb{D}^1(1)$ be a ...
JustSomeGuy's user avatar