Nearest Symmetric Positive-definite Matrix
Find nearest (in Frobenius norm) symmetric positive-definite matrix to A.
nearest_spd(A)
A |
square numeric matrix. |
"The nearest symmetric positive semidefinite matrix in the
Frobenius norm to an arbitrary real matrix A is shown to be (B + H)/2,
where H is the symmetric polar factor of B=(A + A')/2."
N. J. Highham
Returns a matrix of the same size.
Nicholas J. Higham (1988). Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications. Vol. 103, pp.103-118.
A <- matrix(1:9, 3, 3) B <- nearest_spd(A); B # [,1] [,2] [,3] # [1,] 2.034900 3.202344 4.369788 # [2,] 3.202344 5.039562 6.876781 # [3,] 4.369788 6.876781 9.383774 norm(B - A, type = 'F') # [1] 3.758517
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