# All Questions

7,951 questions
Filter by
Sorted by
Tagged with
1k views

### What is the deterministic counterpart of Robbins-Monro algorithm?

From Wikipedia, assume that we have a function $M(x)$, and we want to solve the equation $M(x) = 0$. But we cannot directly observe the function $M(x)$, we can instead obtain measurements of the ...
4k views

### When is building a cluster in the cloud cheaper than building one in my lab for MD simulations?

An Amazon EC2 compute cluster costs about \$800-\$1000 (depending on duty cycle) per physical CPU core over the course of 3 years. In our last round of hardware acquisition, my lab picked up 48 cores ...
198 views

### Solving PSD matrix in Newton's method

I have functions defined as follows: $f1(A) = \sum\|x_i-x_j\|_A = \sum\sqrt{(x_i-x_j)^TA(x_i-x_j)}$ and $f2(A) = \sum\|x_k-x_l\|^2_A$ where A is PSD matrix, x are number vectors. Task is to minimize ...
2k views

### Efficiency of using petsc4py vs. c/c++/fortran

How much slower is petsc4py vs c/c++/fortran? I realize it will depend significantly on the code being executed, but what about something simple like a matrix-vector product?
1k views

### How do I vectorize this 4-D matrix operation in Matlab?

I need to do a large number of matrix operations in Matlab, but one of the matrices is 4-D and my normal instincts for correct vectorization are failing me. Right now I'm using a loop. Maybe somebody ...
1k views

### Decomposition methods for solving large optimization problems

I was wondering if anybody had any suggestions for texts or survey articles on decomposition methods (e.g. primal, dual, Dantzig–Wolfe decompositions) for solving large mathematical programming ...
2k views

### Hill climbing and coordinate descent/ascent

From Wikipedia: In computer science, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an ...
164 views

### Permissive Math Library for Parameter Statistics in C++

I am looking for recommendations for a C++ math library, with a permissive licence, well suited to calculating a wide variety of statistics on segmentations of timebased parameter data. I would be ...
5k views

### Newton-Raphson method for nonlinear partial differential equations

For the numerical solution of Reynolds equations (a non-linear partial differential equation), the Newton-Raphson method is generally proposed. After getting algebraic equations from a finite ...
1k views

### Blaze linear algebra library?

The paper "Expression Templates Revisited: A Performance Analysis of Current Methodologies" in SIAM Journal of Scientific Computing references the "Blaze" linear algebra library. I haven't heard of it ...
4k views

### Meaning of (meta)heuristic methods

For optimization, from Wikipedia: In computer science, metaheuristic designates a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard ...
872 views

### Meaning of search methods and optimization methods

I was wondering what differences and relations are between "search methods" and "optimization methods"? Especially when solving an optimization problem? I emphasize the context of solving ...
5k views

### Implicit finite difference schemes for advection equation

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/...
217 views

### Is it possible to run a Solver Foundation solver against a model containing linear and non-linear elements?

This is a follow up question to one I made previously about non-linear equations and ranged real numbers in Solver Foundation. I acknowledge that where possible, rewriting a problem that is non-...
1k views

### Is lattice Boltzmann suitable for simulation of incompressible Stokes flow?

We have a flow that is dominated by adhesion forces from the substrate and surface tension from the free surface. The material is nearly solid and at rest first, and gets a bit less solid by heating. ...
161 views

### System Speed - Refactoring [closed]

Could the runtime of methods within a system potentially be reduced via refactoring during development (pre-public release)? i.e. Let's assume that methodX() takes ...
1k views

### How to generate neighbors in hill climbing algorithm?

Hill climbing seems to be a very powerful tool for optimization. However, how to generate the "neighbors" of a solution always puzzles me. For example, I am optimizing a solution $(x_1, x_2, x_3)$. ...
2k views

### Algorithms for a many-to-many generalized assignment problem

I can't seem to find any literature on algorithms which can be used to solve a many-to-many generalized assignment problem (GAP), i.e. models where not only can more tasks be assigned to one agent, ...
2k views

### Calculating Lagrange coefficients for SVM in Python

I'm trying to write a full SVM implementation in Python and I have a few issues computing the Lagrange coefficients. First let me rephrase what I understand from the algorithm to make sure I'm on the ...
102 views

### How do you change the desired accuracy of a TS object in PETSc?

I'm currently getting very long propagation times when attempting to use the Time Stepping propagators in Petsc 3.2, and in the interest of speeding things up, I'm curious how I can reduce the ...
779 views

### Practical efficacy of parallel back substitution

The fact that the back substitution is not done in parallel is not important, because it uses a negligible amount of computer time when N is large, compared to the forward elimination. This is a ...
4k views

### What is the best way to find discontinuities of a black-box function?

It was suggested that this might be a better place for this question than Mathematics Stack Exchange where I asked it before. Suppose one has a black-box function which can be evaluated anywhere (...
151 views

### Simplifying some operations on Gram matrices

Suppose two Gram matrices are given $A, B\in\mathbb{R}^{n\times n}$, such that $$A=XX^T,~~~~~~~~~~~~~B=YY^T,$$ for some $X, Y\in\mathbb{R}^{n\times k}$, $k\ll n$. Also, suppose a Gram matrix based on ...
1k views

### Making a Molecular editor/visualizer: Object oriented programming, data structures, and molecules

I am new to programming and I am trying to solve my first big problem and write my first big program. I have looked for open source examples of code to learn from, but so far have only found code in ...
382 views

### Generalized least squares gradient of a vector field

For computing the gradient of a scalar field, one can use the weighted least squares method as described in the paper Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured ...
114 views

### Matching Similar Items from a Set

I'm trying to match items. Given a set of $n$ items I can rank on a scale from 0 to 100 of how similar they are to one another. For instance, if item $n_1$ is milk and item $n_2$ is also milk, then ...
157 views

2k views

### Where do the laws of quantum mechanics break down in simulations?

As someone who holds a BA in physics I was somewhat scandalized when I began working with molecular simulations. It was a bit of a shock to discover that even the most detailed and computationally ...
I have an iterative method for computing the Moore-Penrose generalized inverse of matrices, that is $$X_{k+1} = ((I-\beta X_{k}A)^t) + X_{k}$$ with initial approximation: $$X_{0} = \beta AA^t$$ ...