# All Questions

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407 views

### LAPACK - singular matrices - what does the positive integer info mean?

please can you help me with my code - I use Lapack to solve complex matrix (quite biq) and do it in two steps: I call zgetrf (LU factorization) and then ...
132 views

### Modification of Levinson algorithm for hermitian toeplitz matrix

I have implemented Levinson algorithm for toeplitz matrix by book: Blahut "Fast algorithms for digital signal processing". Book said - modification of this algorithm for Hermitian matrices is simple ...
1k views

### How to use eigenvalue information to efficiently diagonalize matrices?

I apologize if this question in a more general form has been asked before. I have a tridiagonal Toeplitz matrix $K$, whose eigenvalues and eigenvectors are known analytically for any dimension $N$ ....
699 views

### Hash-like algorithm with “weighted” input

The title is not the best but since I have no clue what I'm actually searching I simply used something broad. I'm searching for a an algorithm, a class of algorithms or at least keywords I can use for ...
172 views

### Ways to speed up the computations

OK, I have a FORTRAN code which numerically integrates equations of motion for large data sets of initial conditions. I run this program in my PC and it requires about 1 day of computations per data ...
100 views

### How can I efficiently position the different segments of a large vector in Eigen C++?

I have a very large(up to 9 000 000) VectorXi vector defined in Eigen C++ which is read from a data file. The vector consists of 0, 1, 2, ...n segments with ...
1k views

### Solver suggestion for many small quadratic problem in C++

I have a C++ program/model that in some parts already use IPOPT (with ADOL-C and ColPack) to solve some pretty large non linear problems. Now in an other part of the program I need to solve a large ...
69 views

### Geographic distance between two regions

I am currently trying to calculate the geographic distance between two regions as I want to correlate it with their similarity of another aspect (e.g., similarity in word usage). Currently, I have ...
210 views

### Conjugate residual/gradient convergence checking in practice

Let's say we want to solve $Ax=b$ ($A$ symmetric positive /semi/definite) with the conjugate residual/gradient method. $A$ comes from FEM where the mesh is being refined. The exact solution is $x_*$ ...
54 views

### Calculating the number of molecules diffusing out of a volume [closed]

I have a system of reactions that are governed by differential equations. They are reacting inside of a volume with known dimensions i.e lbh. I don't have any other information on their position ...
1k views

### Convexity Check

I have the following optimization problem and I am trying to check for its convexity. link As per the definition of convexity, "a continuous twice differentiable function is convex ON a convex set, ...
243 views

### Gauss-Seidel, SOR in practice?

When I learned about SOR, it was mostly given as one of the first examples of iterative methods, and then later the iterative methods that I would end up using would be Krylov subspace methods. Are ...
2k views

### Python: Grid with step control ODE solver

I have a problem in physics formulated via an ODE. Now I like to solve it numerically using Pythons scipy.integrate and the therein complex_ode. I figured out how and it works but now I like to ...
667 views

### Using fixed point iteration to decouple a system of pde's

Suppose I had a boundary value problem: $$\frac{d^2u}{dx^2} + \frac{dv}{dx}=f \text{ in } \Omega$$ $$\frac{du}{dx} +\frac{d^2v}{dx^2} =g \text{ in } \Omega$$ $$u=h \text{ in } \partial\Omega$$ My ...
2k views

### Algorithm for solving an ODE with time-dependent parameter numerically

Would anyone please explain me what is the mathematical algorithm to solve a IVP system of ODE with a time-dependent parameter. e.g. ...
2k views

### How to plot orbit of binary star and calculate its orbital elements?

I have a set of dates, position angles ($\theta$) and angular separations ($\rho$) for visual binary star. For example: ...
259 views

### zero pressure gradient flat plate CFD++

I'm trying to perform a trasient simulation of a subsonin flow over a flat plate in CFD++. I want to impose a ramp profile on the velocity at the inlet, like for instance a smooth step, and look at ...
652 views

### Immersed boundary method

I'm trying to use immersed boundary method for the 3D flow problem (Navier-Stokes equations), but I'm maybe misunderstood something in this method. Main principles I took from this book. I use the ...
561 views

### Affect of approximating a non-differentiable function on optimisation of minimisation

I am looking at a problem of constrained minimization, where the function to be minimized contains the Heaviside function, and as such is not twice continuously differentiable. My question is what ...
4k views

188 views

### Is it possible to generalize the two view Sampson error to multiple view cases in computer vision?

In multiple view geometry of computer vision, there is a geometric error called Sampson error which is very useful in the nonlinear estimation of fundamental matrix....