# All Questions

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### Sparse least squares with a (black-box) ill-conditioned operator

It was suggested on math.stackexchange.com that I try to ask this question here. Consider a bounded linear operator $A : U \to V$ where $U$ is finite dimensional and where $V$ is a separable Hilbert ...
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### Mineral dissolution and solute transport around a solid

I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite). The governing equation for transport is the advection-diffusion equation, given as: ...
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### How to troubleshoot numerical instability using finite difference for steady-state non-linear heat conduction equation

I have a problem which I believe is numerical instability when trying to solve a heat conduction equation using finite difference. The short version is that when the parameter $I=80.3$ I get the blue ...
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### VMD polymer draws multiple bonds [closed]

I'm new to VMD and I'm having some problems with displaying my polymer chain. Instead of just one bond, VMD draws multiple bonds. Why does this happen?
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### Decomposing a banded matrix

Suppose we have a linear algebra problem with a banded matrix A which has nonzero entries on the main diagonal, two nearest sub-diagonals, and two other sub-diagonals (such band structure often arises ...
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### Generalization of eigendecomposition problem

Let $A\in \mathbb{R}^{n\times n}$ and $v \in \mathbb{R}^n$. We recognize $Av=\lambda v$ for some scalar $\lambda$ as an eigendecomposition problem. Suppose $\mu \in \mathbb{R}^n$, and let $\odot$ ...
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### Hypergeometric function $_2F_1(z)$ with $|z| > 1$ in GSL

I need to evaluate the hypergeometric function $_2F_1$ with $|z| > 1$ as in Wolfram Language with GSL but the GSL documentation says the $_2F_1$ needs $|z| < 1$. Is there any way I can use GSL ...
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### How to position oneself, if one has little practical engineering background or function, but may have a broader insight into mathematical modeling?

How to position oneself, if one has little practical engineering background or function, but may have a broader insight into mathematical modeling? Or, lets say: I could write models to prove ...
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### Find tuples of points from multiple sets

Given n sets of points in general position in dimension 2 (n typically small, 2-6), can one find tuples of points, one from each of the sets, which are close in some sense (the closest, mutual ...
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### What are some good strategies to test a floating point arithmetic implementation for double numbers?

For IEEE, the single representation is 1-bit sign, 8-bit exponent and 23-bit mantissa. This means that at each exponent value, you can test all 2^23-1 (roughly 9mil cases) possible combination of ...
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### Increasing V-cycles for constant Coarsest Grid Size and increasing Fine Grid size

Problem statement I implemented geometric multigrid for $-\nabla^{2}=f$ where $f=\frac{3\pi^{2}}{4}sin \frac{\pi x}{2} sin \frac{\pi y}{2} sin \frac{\pi z}{2}$ on $\Omega \in [0,1]$ on a unit cube. ...
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### Differences between Two-Grid Correction and V-Cycle Scheme

I found in A Multigrid Tutorial: Second Edition by William L. Briggs‏, Van Emden Henson‏, Steve F. (here) the following Schemes: Two-Grid Correction Scheme, p. 37: And V-Cycle Scheme, p. 40 I want ...
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### Calculations on discontinous grids

Suppose for a grid-based calculation a grid is used such that the grid Jacobian is discontinuous. For example, in 1D, for a domain $x \in$ [0,1], one half of the domain is covered uniformly by twice ...
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### Comparing block versus non-block Krylov methods for handling multiple right-hand-sides

Suppose I wish to solve a linear system $AX=B$ iteratively where $A$ is an $m\times m$ matrix and $X,B$ are $m \times s$ matrices (not single vectors). Instead of solving $s$ independent systems I'm ...
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### How to stack N boxes of varying heights into M stacks, most evenly

The "standard" box-stacking algorithm(s) AFAIK assume a single stack and try to put the "largest" boxes on the bottom. The case I want to solve is simply to distribute the N boxes ...
3k views

### How to find the nearest/a near positive definite from a given matrix?

I'm given a matrix. How do I find the nearest (or a near) positive definite from it? The matrix can have complex eigenvalues, not be symmetric, etc. However, all its entries are real valued. The ...
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### Worst Case complexity of a search engine algorithm

Computer make it possible to find information in large databases. However, the results are often too large to be returned in their entirety to the user who requests them. Computer therefore sort the ...
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### Solve Rational Equation for Root Music in MATLAB

I'm trying to estimate DOA in the Hybrid architecture using root music so I need to solve the attached equation to find the roots for the Root_Music equation in Matlab. Does anyone have an idea for ...
105 views

### Any literature that extensively discusses the ability to strongly inter-/extrapolate computationally on little empirical data?

Any literature that extensively discusses the ability to strongly inter-/extrapolate computationally on little empirical data? This topic has fascinated me, but I find that it seems a bit novel. ...
115 views

### deal.ii - ParaView "warp by scalar" of my output is not continuous

During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in ...
962 views

### Numerical computation of Lyapunov exponent

I'm trying to compute the Lyapunov exponent for a smooth continuous time dynamical system(say, $\dot{\bar{x}} = f(\bar x)$). I using the QR decomposition method. Here are the steps that I follow. ...
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### Numerical scheme HJB equation

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...
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### Approximating the boundary between two sets of points (in 2D): Fitting a region

Given two sets of points $p_{\text{in},i}$ and $p_{\text{out},j}$ inside and outside of what I intuitively call a "region", I would like to estimate and describe the boundary of this region. ...
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### Identifying Noetherian symmetries from general Lie symmetries of a differential equation

I know the Lie symmetry group of the harmonic oscillator differential equation from the literature. It is an 8 parameter Lie group. 5 of these generators generate Noether symmetry: G_1=\sin(2t)\frac{...
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### Contact analysis does not converge due to the projection falls outside valid domain

I implemented Node-To-Surface contact algorithm (Wriggers, Peter, Computational contact mechanics., Berlin: Springer (ISBN 3-540-32608-1/hbk). xii, 518 p. (2006). ZBL1104.74002.). The code is done by ...
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### How to use plot command in fenics [closed]

I'm new to Fenics and want to understand the plot command. My code: ...
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### How do I find the minimum-area ellipse that encloses a set of points?

I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...
The aim is to solve the below equations and plot $m$ with time, i.e. $\frac{dm}{dt}$ $k$ is unknown and needs to be estimated. For the parameter estimation, the below values in the table for m versus ...
The test functions of general finite elements are like interpolation functions (if my understanding is correct). But how about test functions of Raviart-Thomas elements? Let's raise the $RT0$ element ...