Questions tagged [numerical-analysis]
The numerical-analysis tag has no usage guidance.
23
questions with no upvoted or accepted answers
11
votes
0answers
1k 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 \...
9
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
...
8
votes
2answers
800 views
Is “ternary search” an appropriate term for the algorithm that optimizes a unimodal function on a real interval?
Suppose that I want to optimize a unimodal function defined on some real interval. I can use the well-known algorithm as described in Wikipedia under the name of ternary search.
In case of the ...
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
707 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
282 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
383 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
113 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
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
149 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
2answers
69 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
82 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
31 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
42 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
43 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
68 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
446 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 ...
