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### Convergence of fixed point iterations of a non-linear matrix system

I'm working on modeling two phase immiscible flow in a porous medium. When I setup the system of equations, I obtain a non-linear system of equations that can be expressed in the form: $A(x)x=b$ ...
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### CVXOPT VS. OpenOpt

CVXOPT: http://abel.ee.ucla.edu/cvxopt/index.html OpenOpt: http://openopt.org/Welcome What's the relation between them? What are the advantages/disadvantages of them, respectively? BTW, is there any ...
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problem comes from "Numerical solution of fractional integro-differential , equations by collocation method , E.A. Rawashdeh, Department of Mathematics, Yarmouk University, Irbid 21110, Jordan" $D^... 1answer 87 views ### neural networks: multilayer on-off perceptrons This article says that all any multilayer perceptron with a linear on-off functions for all the neurons can be reduced to a two-layered perceptron. Now, consider a two input/one output perceptron. ... 3answers 1k views ### Numerical methods for discontinuous r.s. ODEs what are state of art methods for numerical solution of ODEs with discontinuous right side? I'm mostly interested piecewise-smooth right side functions, e.g. sign. I'm trying to solve the equation of ... 1answer 160 views ### FEM simulation of a material being stretched I'm trying to teach myself FEM. The problem I have in mind is to completely investigate a plastic (e.g rubber band) being stretched (therefore, boundary conditions move as you stretch). I imagine this ... 2answers 106 views ### How can you explain the following bound on the inner product? I am reading a paper on stability of CG, and I came across the following statement: \begin{equation} \frac{\|A\|\,\|p\|^2}{\langle p,Ap\rangle} \leq \kappa(A) \end{equation} where$\kappa(\cdot)$is ... 1answer 54 views ### Finding most informative feature subsets given dataset, clustering algorithm and gold standard partition I have an$n \times m$matrix of data$\mathbf{D}$as well as a$k$-partition$P$of$n$indices each representing a row in a dataset. Assuming an arbitrary clustering algorithm$A$, I would like to ... 2answers 409 views ### Task-based shared-memory parallel libraries in Scientific Computing In recent years, several libraries/software projects have appeared that offer some form or another of general-purpose data-driven shared-memory parallelism. The main idea is that instead of writing ... 2answers 2k views ### Gram-Schmidt method to identify linearly dependent vectors A method to orthogonalize a set of vectors (vectors of unit length that are mutually orthogonal) is the Gram-Schmidt process: http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Note that the ... 1answer 7k views ### Understanding the Wolfe Conditions for an Inexact line search According to Nocedal & Wright's Book Numerical Optimization (2006), the Wolfe's conditions for an inexact line search are, for a descent direction$p$, Sufficient Decrease:$f(x+\alpha p)\le f(x)+...
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After reading the first answer here about how the best way to find the most performant sparse solver is to try almost everything, I began to wonder if there was any past work on libraries or research ...
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### Convergence of the gradient descent and linear vs non-linear fixed point iteration

Suppose a system $$Ax=b$$ is given, with $A\in\mathbb{R}^{n\times n}$ being a symmetric positive-definite matrix, and some non-zero $b\in\mathbb{R}^n$. The gradient method with optimum step length can ...
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### How to choose a method for solving linear equations

To my knowledge, there are 4 ways to solving a system of linear equations (correct me if there are more): If the system matrix is a full-rank square matrix, you can use Cramer’s Rule; Compute the ...
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### Impose the compatibility conditions for mixed finite elements method in Stokes equation

$\newcommand{\v}{\boldsymbol{#1}}$ Suppose we have following Stokes flow model equation:  \tag{1} \left\{ \begin{aligned} -\mathrm{div}(\nu \nabla \v{u}) + \nabla p &= \v{f} \\ \mathrm{div} \...
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### Using same memory space for global and local Petsc DA Vectors

I have constructed a local and global distributed array in Petsc 3.2 using: DMCreateGlobalVector(da, &v); DMCreateLocalVector(da, &lv); In order to ...