Questions tagged [numerical-analysis]
The numerical-analysis tag has no usage guidance.
24
questions with no upvoted or accepted answers
11
votes
0answers
2k views
Alternatives to SVD for rank factorization
I have rank-deficient matrix $M \in \mathbb{R}^{n\times m}$ with $\text{rank}(M) = k$ and I want to find a rank factorization $M = PQ$ with $P \in \mathbb{R}^{n \times k}$ and $Q \in \mathbb{R}^{k \...
10
votes
0answers
1k views
Does Automatic Differentiation handle conditional branches, if yes how?
I'm trying to understand how Automatic Differentiation (AD) works.
For simple algebraic operation, I get the chain rule thing.
But, when the code contains conditional statement like
...
5
votes
0answers
60 views
Testing whether an analytic function vanishes identically
I have an application that basically reduces to testing whether a given function vanishes identically. The function is given symbolically, using unary and binary operators on complex numbers. For ...
5
votes
0answers
719 views
Arc-Length parameterization of a cubic bezier curve
I like to implement an arc-length Parameterization of a cubic bezier curve. So far I have implemented the method of calculating the arc length of the curve and now I'm stuck at calculating the times ...
3
votes
0answers
311 views
Stable and fast computation of the squared euclidean distance matrix
Let's say I want to compute the matrix $M$ of the squared euclidean distances between each pair of vectors $(x, y)$ belonging to two sets $X$ and $Y$ respectively. The sets of vectors $X$ and $Y$ have ...
3
votes
0answers
385 views
Cyclic coordinate method: how does it differ from Hook & Jeeves and Rosenbrock?
I have trouble understanding the cyclic coordinate method. How does it differ with the Hook and Jeeves method and the Rosenbrock method?
From a past exam text:
Describe the cyclic coordinate ...
2
votes
0answers
124 views
Avoiding loss of significance without series expansion
I have a problem on an assignment where I have to reduce the loss of significance due to subtraction for a function
$$\frac{\sin(x)}{x-\sqrt{x^2-1}}$$
without using a series expansion. I can get ...
2
votes
0answers
67 views
0 error interpolation for discrete finite value points
I am working on an algorithm that requires me to interpolate a couple trillion positive discrete points with f(x) having low finite value (for example 0 - 5). It there a specialized algorithm specific ...
1
vote
0answers
23 views
Finding points of local maximum error in Remez algorithm
So the Remez algorithm is an algorithm for finding optimal polynomial approximations or at the very least for converging towards them. To find an approximation of $f$ by an $N$th degree polynomial the ...
1
vote
0answers
19 views
Are there practical usage of determinants in numerical simulation?
I know the historical importance of the link between linear systems and determinants. I also know that determinants have a beautiful connection with non-singular matrices, i.e., if a matrix is non-...
1
vote
0answers
46 views
Accuracy and performance between a division and subtraction for a ratio in decibels
For comparing two images, one can use the Peak Signal-to-Noise Ratio (PSNR) metric, defined as follows:
$\mathrm{PSNR} = 10 \cdot \log_{10}\left(\frac{\mathrm{MAX}^2}{\mathrm{MSE}}\right) = 20 \cdot \...
1
vote
0answers
69 views
Sparse Matrix inversion without actual inversion
I want to know what are the efficient way to invert a Sparse Matrix? Are there any algorithm,linear algebra or expansions that make this task easier with out actually inverting the matrix?
Thank you ...
1
vote
0answers
26 views
Construct unitary $Q$ such that $span\{q_1,q_2\} = span\{v_1,v_2\}$ where $v_1,v_2 \in \mathbb{R}^n$ are given as input
Assume also that $v_1,v_2$ are linearly independent, and $q_i \in \mathbb{R}^n$ denotes the $i$-th column of $Q$. This is what I've got so far. First obtain unit vectors $w_1,w_2$ which are orthogonal ...
1
vote
0answers
154 views
predictor/corrector and gear integration for positive and negative time steps
I have a predictor method that takes differential equations for 214 biological species and integrates them in time using positive time steps. Right now it is able to successfully integrate the ...
0
votes
0answers
9 views
Sparse Recovery and Feature Selection
This may be a silly question but are sparse recovery and feature selection problems fundamentally the same? Namely, say we have a set $N$ of features and $S \subset N$ which are the "important&...
0
votes
2answers
84 views
How to determine the set of real numbers corresponding to a given floating point number?
Let's say we consider IEEE 754 double precision floating-point numbers, and we use RNTE - Round To Nearest, Ties to Even - rounding.
I know that the RNTE rounding works this way:
given two consecutive ...
0
votes
2answers
97 views
Numerical Approximation in Java
I am trying to solve an equation which I believe cannot be done analytically, but can use a numerical approximation to get a result. The equation is:
$$\frac{2*\sqrt{\pi}*h*s*e^{m^{2}/(2*s^2)}}{\sqrt{...
0
votes
0answers
32 views
Normalizing the Central Difference Method
How could I normalize the 2nd order central difference method?
The original function is F(A,B,C,D) and only one variable is varied at a time. ie
$F'' = \frac{F(A+\Delta A,B,C,D) - 2\times F(A,B,C,D) +...
0
votes
0answers
43 views
How to solve the following problem by using Gaussian elimination with partial pivoting (A=PLU)?
****The Question is here***** (in the link)
Given a nonsingular matrix A $\in$ $R^*(nxn)$, how would you solve the following problems efficiently using Gaussian elimination with partial pivoting (the ...
0
votes
0answers
36 views
Application of iterative algorithm $(\theta_n,w_n)$ converging to $\{(\theta,\theta):\theta \in \Bbb R\}$
I have a iterative algorithm $(\theta_n,w_n)$ which I am showing converges to $\{(\theta,\theta):\theta \in \Bbb R\}$.
The iterative algorithm is of the form :
$\theta_{n+1} = \theta_n + a(n)[h(\...
0
votes
0answers
44 views
Computational cost of using dictionary in floating point opertations
I would like to know the computational cost of using/accessing a dictionary.
This should depend on the length of the dictionary. Say a dictionary $D$ has $n$ elements.
What would be the cost of ...
0
votes
0answers
77 views
Naviers Stokes equation and machine learning
I am looking for a reference explaining how to solve Navier-Stokes numerically using Machine learning algorithms .
Thank you in advance for your help .
0
votes
0answers
19 views
Numerical analysis - f(x) = f(y)
I am writing a function that can be split into cases
(1)$f(x) \leq f(y)$ and $f(x) \geq f(y)$
or into cases
(2)$f(x) < f(y), f(x) = f(y), f(x) > f(y)$
If I have f(x) = f(y), it is ...
0
votes
0answers
466 views
Most stable algorithm to solve a system of linear equations?
I am doing some image processing involving solving a system of linear equations. I am getting some errors and bits of the image looks corrupted. I would like to know what is the most stable way to ...
