# All Questions

8,358 questions
Filter by
Sorted by
Tagged with
9 views

### Hit-n-Run Monte Carlo on convex polytope

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
21 views

### Efficient ways to numerically evaluate matrix exponentials

What are some computationally efficient ways to solve matrix exponentials, i.e. functions of the form : f(X)=$e^{X}$, where X is a square matrix ? So far I have been able to diagonalise some ...
10 views

### HSS preconditioner with gmres

I have question about HSS preconditioner with GMRES method. For implementing the HSS preconditioner with GMRES, we need to solve the linear system of the form (I + H)(I + S)z =r, for a given r at each ...
17 views

### Using adolc for the sign function in c++

Here is an implementation of the sign function in C++ using Adolc librairy for automatic differentiation. ...
19 views

### Determinant of a matrix after removing or adding lines and columns

In quantum mechanics, the wavefunction of N electrons is given by a determinant. I am working on a Monte Carlo algorithm. At each Monte Carlo step, I need to add or remove an electron, which means ...
25 views

### Inverting really big symmetric block matrix

I have a really big symmetric 7.000.000 X 7.000.000 matrix that i would like to invert. The matrix is extremely sparse and it can be rearranged as to become a block matrix. The biggest blocks are ...
22 views

### Why the two Gram-Schmidt algorithms produce different results for qr factorization?

For the qr factorization using classic Gram-Schmidt algorithm, I found the 2 different implementations below. The first one uses the for loop to compute the upper ...
33 views

### pdepe or Crank-Nicolson? How much is pdepe good?

I am beginner in MATLAB and similar. I sow and discussed with my professors doing simulations some times: they wrote down a lot of calculus, most of them using Crank-Nicolson Method and so implement ...
75 views

### How to compute over 1 billion particles?

I want to simulate human erythrocytes in capillaries. I calculated, that for 1 meter long and 1 mm in diameter capillary there are about 3 billions blood cells. Erythrocytes are actually discs, but ...
48 views

### Why the solid FEM problem can not be solved after constraining 3 degrees of freedom?

I write a simple MATLAB code for solving solid FEM problem. The problem looks like that (1) (2) x-------x | / | | / | | / | x-------x (3) (4) ...
8k views

### why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...
48 views

### Is the similar subdivision of a delaunay mesh still delaunay?

I have a delaunay triangulation for a 2d box with say an airfoil inside. If I uniformly refine this mesh by subdividing each triangle in the mesh into 4 triangles by halving each edge, is the ...
26 views

### How to compute the gradient of T with Armadillo library [closed]

I am using the Armadillo library to solve a 3d heat conduction problem on 3d unstructured grid system,the gradient of the T field is determined by the least square method. I have created a matrix ...
46 views

### Is it possble to do this complex symbolic calculation with Matlab?

Sorry it's bit abrupt, but recently I am caught up in some symbolic calcualtion which is tedious and almost impossible with mere human hands, so just wondering is it possible to solve the double ...
5 views

### Change value of dependent sweep varietals

I am using Comsol to model a really hard problem. I am using the sweep for one variable (width), and as the problem state (Length=2*width). When I use the sweep the value of Length does not update. ...
652 views

### Example where autodiff works but symbolic differentiation will not?

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...
94 views