Posts Tagged ‘ Calculus ’

Numerical analysis for statisticians

August 25, 2011
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Numerical analysis for statisticians

“In the end, it really is just a matter of choosing the relevant parts of mathematics and ignoring the rest. Of course, the hard part is deciding what is irrelevant.” Somehow, I had missed the first edition of this book and thus I started reading it this afternoon with a newcomer’s eyes (obviously, I will

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Example 8.36: Quadratic equation with real roots

April 29, 2011
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Example 8.36: Quadratic equation with real roots

We often simulate data in SAS or R to confirm analytical results. For example, consider the following problem from the excellent text by Rice:Let U1, U2, and U3 be independent random variables uniform on . What is the probability that the roots...

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Single variable optimization

January 1, 2011
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Optimization means to seek minima or maxima of a funtion within a given defined domain.If a function reach its maxima or minima, the derivative at that point is approaching to 0. If we apply Newton-Raphson method for root finding to f’, we can get the optimizing f.Read More: 223 Words Totally

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Single variable optimization

January 1, 2011
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Optimization means to seek minima or maxima of a funtion within a given defined domain.If a function reach its maxima or minima, the derivative at that point is approaching to 0. If we apply Newton-Raphson method for root finding to f’, we can get the optimizing f.Read More: 223 Words Totally

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one-dimensional integrals

December 25, 2010
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one-dimensional integrals

The foundamental idea of numerical integration is to estimate the area of the region in the xy-plane bounded by the graph of function f(x). The integral was esimated by divide x to small intervals, then add all the small approximations to give a total approximation.Read More: 468 Words Totally

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one-dimensional integrals

December 25, 2010
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one-dimensional integrals

The foundamental idea of numerical integration is to estimate the area of the region in the xy-plane bounded by the graph of function f(x). The integral was esimated by divide x to small intervals, then add all the small approximations to give a total approximation.Read More: 468 Words Totally

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Root finding

December 4, 2010
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Numerical root finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limits which is a root. In this post, only focus four basic algorithm on root finding, and covers bisection method, fixed point method, Newton-Raphson method, and secant method.Read More: 1886 Words Totally

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Root finding

December 4, 2010
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Numerical root finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limits which is a root. In this post, only focus four basic algorithm on root finding, and covers bisection method, fixed point method, Newton-Raphson method, and secant method.Read More: 1896 Words Totally

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