Joshua Burkholder

Mathematics and Computer Science

Three-Dimensional Givens Rotations

By Joshua Burkholder July 14, 2019 Givens Rotation Matrices, Mathematics No Comments

Note: The math on this page is progressively rendered. It can take up to 45 seconds before the final rendering…

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Online Weighted Mean

By Joshua Burkholder April 22, 2014 Mathematics No Comments

Given the following set of inputs and their associated weights: {(x1,w1),(x2,w2),…,(xn−1,wn−1),(xn,wn)} Let n be the number of inputs and their…

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Online Covariance

By Joshua Burkholder October 26, 2013 Mathematics 3 Comments

Given the following set of two-dimensional inputs: {(x1,y1),(x2,y2),…,(xn−1,yn−1),(xn,yn)} Let n be the number of two-dimensional inputs, X represent the x…

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Online Variance

By Joshua Burkholder October 20, 2013 Mathematics 1 Comment

Let n be the number of values, vn be the biased sample variance of the first n values, vn−1 be…

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Two-Dimensional Givens Rotation

By Joshua Burkholder September 29, 2013 Givens Rotation Matrices, Mathematics No Comments

The following matrix is the two-dimensional Givens Rotation from the x axis to the y axis: (cos(θ)cos(θ+90°)sin(θ)sin(θ+90°))(cos(θ)cos(θ+π2)sin(θ)sin(θ+π2))(cos(θ)−sin(θ)sin(θ)cos(θ)) This matrix rotates…

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