# Questions tagged [numerics]

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### What is a relative condition number of a sum of positive values?

We want to compute the relative condition number of: $$x_1+x_2+x_3+\cdots$$ We assume all values are positive, and we will do a limit of a large $x_1=10^{8}$, and smaller values for all the other ...
0answers
220 views

### Newton - Raphson method : maxima of function in 2 variables

I am computing the maximum of a function (with two-variables) using Newton-Raphson method. The function is : $e^{-(x \ - x_0)^2 - (y \ - y_0)^2}$, whose maxima exists at $(x_0,y_0)$. The Jacobian ...
1answer
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### SIRS Model doesn't depend on initial conditions?

So i have been working (as an undergrad, by working i mean "Redoing a few things my professor does") in a SIRS model for epidemies. SIRS stands here for: Susceptible -> Infected -> Recovered -> ...
1answer
117 views

### Error measure for a simple finite difference scheme

I am responsible for assisting with certain error measurements for an FE program. The idea is to set up some benchmark comparisons which we can use for future development of the program. To simplify ...
0answers
105 views

### Definition of CFL number in Arbitrary Lagrangian-Eulerian framework

In an Eulerian frame of reference, the CFL number is defined as $$\sigma=\frac{u \Delta t}{\Delta x}$$ with $u$ the magnitude of the fluid velocity. A restriction such as $\sigma<1$ for time ...
1answer
246 views

### How to compute the Frobenius norm of matrices whose entries are either too large or too small?

While implementing in Matlab the Frobenius norm of a matrix $$\| A\|_{\text F} := \sqrt{ \sum_{i=1}^m \sum_{j=1}^n a_{ij}^2 },$$ a problem arises when numbers are too big or too small: If a number ...
0answers
86 views

### How to optimize for decay constant in exponential-like function?

I've got a data set of points $M_O .. M_N$ for time points $t_0 .. t_N$, where $N$ is approximately 10-20, and the spacing of time is not uniform (i.e., $t_{i+1}-t_i$ is not constant for all i). It is ...
1answer
277 views

### Numerical calculation sum of exponential functions

I have to repeatedly calculate a function which contains a sum of a large number (~100) of exponential terms: $f(x) = \sum_{r=1}^{100} C_r e^{b_r \cdot x}$ There is no relation between the $C_r$ ...
1answer
252 views

### Clenshaw-type recurrence for derivative of Chebyshev series

The naive summation of a Chebyshev series \begin{align*} f(x) = \frac{c_0}{2} + \sum_{k=1}^{n-1} c_{k}T_{k}(x) \end{align*} which employs the three-term recurrence for evaluation of the Chebyshev ...
1answer
101 views

### finding the growth rate from numerical data

Suppose i have a bunch of 10 data points and i have to conclude whether the increase is $n^2,n^3,\cdots,2^n,3^n, e^n,\cdots$. For example i have the image:- Now the increase is either polynomial or ...
0answers
19 views

### Does excitation type matter in a time-domain simulation/computation of a transfer function of an LTI system?

Let's say I am running a FDTD simulation of a wave-equation to determine a transfer function of an LTI system: \begin{equation} H(f) = \dfrac{Y(f)}{X(f)}\ \end{equation} where $Y(f)$ and $X(f)$ are ...
1answer
124 views

### Using GSL for basic operations

I am learning C/C++ for Scientific Computing and I have a question regarding the usage of scientific libraries for basic operations. Suppose I have to write a small program in C for a bioinformatics ...
2answers
172 views

### Literatures on numerical stability of optimisation algorithms

I am curious of whether optimisation algorithms (whatever simplex, active-set quadratic programming, interior point sequential etc.) can fail due to numerical errors and how to avoid them. But I ...
1answer
118 views

### Reference Request: Raviart Thomas with hanging nodes

I am interested in reading about the analysis (existence, uniqueness, error estimates) of elliptic problems solved with a Mixed method that uses the Raviart Thomas elements (so far so good, easy to ...
3answers
2k views

### Galerkin method: Test functions vs. Basis functions

I'm a novice to finite element and I'm finding quite hard to find the actual difference between Test function(s) and Basis function(s). I would be glad if somone could explain me that and point out ...
1answer
97 views

### interpolation 2D irregular nodes

Given a 2D irregular spaced data like shown in the figure, I would like to know how to find derivatives at '*' by interpolating the values at 'o'. Does lagrange 2D interpolation work at irregular ...
1answer
280 views

### Is there any point to using hypot() for $\sqrt{1+c^2}$, $0 \le c \le 1$ for real numbers

It is conventional wisdom that programmers should use std::hypot whenever one implements an expression of the form $r = \sqrt{x^2 + y^2}$ In my example, my ...
2answers
236 views

### Boundary conditions for streamlines in enclosed flow

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
1answer
120 views

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581 views

### How to construct an ellipsoid using Ansys design modeller (or any other 3D CAD software) [closed]

I am working on numerical simulation of breast model to evaluate the use of thermal imaging for breast cancer detection. To do this I need to construct an ellipsoid rotated 30 degrees around y-axis ...
0answers
810 views

### Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
2answers
68 views

### Bounded approximation to a bounded function

I have a non-negative function $f(x) \ge 0$ defined on the interval $[a,b]$. I would like to have a finite-dimensional approximation to this function that is guaranteed to be non-negative on $[a,b]$. ...
2answers
423 views

### How much regularization to add to make SVD stable?

I've been using Intel MKL's SVD (dgesvd through SciPy) and noticed that results are are significantly different when I change precision between ...