Quadratic Form of the inverse of a matrix and a vector

Description

We compute the quadratic form of a vector and the inverse of a matrix in an efficient manner. Let x be a real vector of length p, and let A be a p x p nonsingular matrix. Then, we compute the quadratic form q = x' A^{-1} x.

Usage

1

Arguments

A

matrix that is p x p and nonsingular

x

vector of length p

Details

A naive way to compute the quadratic form is to explicitly write t(x) %*% solve(A) %*% x, but for large p, this operation is inefficient. We provide a more efficient method below.

Note that we have adapted the code from: http://tolstoy.newcastle.edu.au/R/help/05/11/14989.html

Value

scalar value

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