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Here we discuss an application of HPC (not high performance computing, instead high precision computing, which is a special case of HPC) applied to dynamical systems such as the logistic map in chaos theory. defined as X(k) = 4 X(k) (1 - X(k-1)).
For all these systems, the loss of precision propagates exponentially, to the point that after 50 iterations, all generated values are completely wrong. Tons of articles have been written on this subject - none of them acknowledging the…Continue
Added by Vincent Granville on November 13, 2017 at 7:00pm — No Comments
In this post, we learn about building a basic search engine or document retrieval system using Vector space model. This use case is widely used in information retrieval systems. Given a set of documents and search term(s)/query we need to retrieve relevant documents that are similar to the search query.
The problem statement explained above is represented as in below image. …Continue
Added by suresh kumar Gorakala on November 7, 2017 at 6:30am — No Comments
Here we describe well-known chaotic sequences, including new generalizations, with application to random number generation, highly non-linear auto-regressive models for times series, simulation, random permutations, and the use of big numbers (libraries available in programming languages to work with numbers with hundreds of decimals) as standard computer precision almost always produces completely erroneous results after a few iterations -- a fact rarely if ever mentioned in the scientific…Continue
Added by Vincent Granville on November 6, 2017 at 8:30pm — No Comments
There is no need to get confused with multiple linear regression, generalized linear model or general linear methods. The general linear model or multivariate regression model is a statistical linear model and is written as Y = XB + U.
Usually, a linear model includes a number of different statistical models such as ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The GLM is a generalization of multiple…