# Blog Archives

## Combined Linear Congruential Generators with R

September 7, 2017
By Part of 3 in the series Random Number GenerationCombined linear congruential generators, as the name implies, are a type of PRNG (pseudorandom number generator) that combine two or more LCGs (linear congruential generators). The combination of two or more LCGs into one random number generator can result in a marked... The post Combined Linear Congruential Generators with R appeared first...

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## Multiplicative Congruential Generators in R

August 31, 2017
By Part 2 of 2 in the series Random Number GenerationMultiplicative congruential generators, also known as Lehmer random number generators, is a type of linear congruential generator for generating pseudorandom numbers in . The multiplicative congruential generator, often abbreviated as MLCG or MCG, is defined as a recurrence relation similar to... The post Multiplicative Congruential Generators in R appeared first on...

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## Linear Congruential Generator in R

August 24, 2017
By Part of 1 in the series Random Number GenerationA Linear congruential generator (LCG) is a class of pseudorandom number generator (PRNG) algorithms used for generating sequences of random-like numbers. The generation of random numbers plays a large role in many applications ranging from cryptography to Monte Carlo methods. Linear congruential... The post Linear Congruential Generator in R appeared first on...

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## Simpson’s Rule for Approximating Definite Integrals in R

August 17, 2017
By Part 9 of 9 in the series Numerical AnalysisSimpson’s rule is another closed Newton-Cotes formula for approximating integrals over an interval with equally spaced nodes. Unlike the trapezoidal rule, which employs straight lines to approximate a definite integral, Simpson’s rule uses the third Lagrange polynomial, to approximate the definite integral... The post Simpson’s Rule for Approximating Definite Integrals in R...

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## The Trapezoidal Rule of Numerical Integration in R

August 10, 2017
By Part of 8 in the series Numerical AnalysisThe Trapezoidal Rule is another of Closed Newton-Cotes formulas for approximating the definite integral of a function. The trapezoidal rule is so named due to the area approximated under the integral representing a trapezoid. Although there exist much more accurate quadrature methods, the... The post The Trapezoidal Rule of Numerical Integration in R...

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## Numerical Differentiation with Finite Differences in R

August 3, 2017
By Part 1 of 7 in the series Numerical AnalysisNumerical differentiation is a method of approximating the derivative of a function at particular value . Often, particularly in physics and engineering, a function may be too complicated to merit the work necessary to find the exact derivative, or the function itself... The post Numerical Differentiation with Finite Differences in R appeared...

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## Divided Differences Method of Polynomial Interpolation

July 27, 2017
By Part of 6 in the series Numerical AnalysisThe divided differences method is a numerical procedure for interpolating a polynomial given a set of points. Unlike Neville’s method, which is used to approximate the value of an interpolating polynomial at a given point, the divided differences method constructs the interpolating polynomial... The post Divided Differences Method of Polynomial Interpolation appeared first...

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## Neville’s Method of Polynomial Interpolation

July 19, 2017
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Part 1 of 5 in the series Numerical AnalysisNeville’s method evaluates a polynomial that passes through a given set of and points for a particular value using the Newton polynomial form. Neville’s method is similar to a now-defunct procedure named Aitken’s algorithm and is based on the divided differences recursion... The post Neville’s Method of Polynomial Interpolation appeared first on...

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## Lagrangian Polynomial Interpolation with R

July 13, 2017
By Part 2 of 4 in the series Numerical AnalysisPolynomial interpolation is the method of determining a polynomial that fits a set of given points. There are several approaches to polynomial interpolation, of which one of the most well known is the Lagrangian method. This post will introduce the Lagrangian method... The post Lagrangian Polynomial Interpolation with R appeared first on...

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## Set Theory Ordered Pairs and Cartesian Product with R

July 6, 2017
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Part 5 of 5 in the series Set TheoryOrdered and Unordered Pairs A pair set is a set with two members, for example, , which can also be thought of as an unordered pair, in that . However, we seek a more a strict and rich object that tells us... The post Set Theory Ordered Pairs and Cartesian Product with...

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