All Questions
Tagged with applied-mathematics na.numerical-analysis
11 questions
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 ...
- 502
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 ...
- 879
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 ...
- 11
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 ...
- 351
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 \...
- 135
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'...
user89890
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 ...
- 749
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 ...
- 3,574
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 ...
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 ...
- 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 ...
- 5,327