# All Questions

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16k views

### Dealing with the inverse of a positive definite symmetric (covariance) matrix?

In statistics and its various applications, we often calculate the covariance matrix, which is positive definite (in the cases considered) and symmetric, for various uses. Sometimes, we need the ...
167 views

### Is it possible to represent non-linear ranking type constraints as equivalent linear constraints?

I have formulated a linear program with binary indicator variables $z_i(a)$ which is equal to $1$ if the $i^{th}$ document is of rank $a$ and $0$ otherwise. The other variables in the linear program,...
625 views

### Difficulty with Spectral Method using Chebyshev Polynomials

I am having a bit of difficulty in trying to understand a paper. The paper uses spectral method to solve for an eigenvalue that comes from a system of coupled ODEs. I will write out only one equation ...
1k views

### Computational cost of numerical methods for PDEs

Say I need to solve a PDE numerically. Depending on the problem and the numerical method chosen, I can usually see some issues coming: implementation issues (e.g. boundary conditions, parallelization),...
1k views

### Absolute Value in Linear Constraints

I have the following optimization problem where I have absolute value in my constraints: Let $\mathbf{x} \in \mathbb{R}^n$ and $\mathbf{f}_0, \mathbf{f}_1, \ldots, \mathbf{f}_m$ be column vectors of ...
362 views

### Fastest way to find eigenpairs of a small nonsymmetric matrix on a GPU in shared memory

I have a problem where I need to find all positive (as in the eigenvalue is positive) eigenpairs of a small (usually smaller than 60x60) nonsymmetric matrix. I can stop calculating when the eigenvalue ...
10k views

### Is it a good idea to use vector<vector<double>> to form a matrix class for high performance scientific computing code?

Is it a good idea to use vector<vector<double>> (using std) to form a matrix class for high performance scientific computing code? If the answer is no. ...
203 views

### How to prove that my problem is np-hard

For an assignment i need to program an application to schedule conversations. Something similar to speeddating or Pta meeting. The problem is that i know that this is hard to solve, but i dont know if ...
806 views

### What is the best way to get erfi with scipy?

I want this: http://mathworld.wolfram.com/Erfi.html But apparently scipy does not have this in its extensive special functions library. http://docs.scipy.org/doc/scipy/reference/special.html It is ...
202 views

6k views

### Boundary conditions for the advection equation discretized by a finite difference method

I am trying to find some resources to help explain how to choose boundary conditions when using finite difference methods to solve PDEs. The books and notes which I currently have access to all say ...
180 views

### most adequate edit distance for misspellings in names?

Algorithms for edit distance give a measure of the distance between two strings. Question: which of these measures would be most relevant to detect two different persons names which are actually the ...
190 views

### Is there a backward stable $\tilde{O}(n \log(1/\epsilon))$ algorithm to factor a complex polynomial?

Finding the roots of a complex polynomial is in general extremely numerically unstable, as discussed in (1). According to Pan ((2), (3)), this produces a cubic complexity lower bound, and he presents ...
168 views

### Identifying the name/provenance of a technique to find the nullspace vectors of a matrix by random sampling and the conjugate residual method

I have got a large sparse matrix $A \in \mathbb R^{n \times n}$ and I want to find non-trivial elements in the kernel/nullspace of this matrix. How can this be done? I would like to learn more about a ...
11k views

### MATLAB Code Evaluation for Least Squares Regression (LSR) [closed]

Below is my own approach to implement the Least Squares Regression algorithm in MATLAB. Could you please take a look and tell me if it makes sense; if it does exactly what is supposed to do? EDIT: ...
150 views

### What is a good introduction to mixed quantum-classical modelling

Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
1k views

### Testing numerical optimization methods: Rosenbrock vs. real test functions

There seem to be two main kinds of test function for no-derivative optimizers: one-liners like the Rosenbrock function ff., with start points sets of real data points, with an interpolator Is it ...