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difference between sqrtm and chol
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kumar vishwajeet
Jun 30, 2011, 12:08:07 AM6/30/11
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For calculation of sigma points in Unscented Kalman filter(UKF), we need to take the square root of the covariance matrix. There are two ways to calculate the square root of a matrix:
1. Using cholesky decomposition - works only for positive definite matrix and the result is an upper or lower triangular matrix.
2. Using sqrtm - works for positive semidefinite as well. The result is a dense matrix.
I have observed that for Positive definite matrices, the eigen values of the matrix obtained by cholesky decomposition and by using sqrtm are same. It means that the matrices obtained by the two method is identical for positive definite covariance matrix.
I want to ask :
1. can we use "sqrtm", in general, for finding the square root of a matrix??
2. People using UKF, in general, use "chol" to find the square root. What could be the reason?? What could be the reason?? I mean why not use "sqrtm" as it provides the square root even if the matrix is not positive definite.
1. Using cholesky decomposition - works only for positive definite matrix and the result is an upper or lower triangular matrix.
2. Using sqrtm - works for positive semidefinite as well. The result is a dense matrix.
I have observed that for Positive definite matrices, the eigen values of the matrix obtained by cholesky decomposition and by using sqrtm are same. It means that the matrices obtained by the two method is identical for positive definite covariance matrix.
I want to ask :
1. can we use "sqrtm", in general, for finding the square root of a matrix??
2. People using UKF, in general, use "chol" to find the square root. What could be the reason?? What could be the reason?? I mean why not use "sqrtm" as it provides the square root even if the matrix is not positive definite.
Thanks.
prasha...@gmail.com
Nov 29, 2013, 10:01:39 AM11/29/13
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but i am facing a problem about for using chol(P) command.
lets see whether your sqrtm works or not..
Joel
Sep 10, 2014, 8:15:27 PM9/10/14
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"kumar vishwajeet" wrote in message <iugsr7$mq5$1...@newscl01ah.mathworks.com>...
Most square matrices M such as this one have many square roots. For example, if there is an eigenvalue decomposition of one matrix square root A, then changing the sign of ANY of the non-zero eigenvalues of A produces another matrix whose square is M. So if M is KxK and non-singular, then in general it can have 2^K distinct matrix square roots.
The difference between CHOL and some other functions that compute square roots of matrices is that CHOL is somewhat faster than most of them, typically by a factor ~ 2 or 3. However, some of the others (QR, SVD, EVD) have other advantages, such as orthogonal columns. So I do not know if CHOL is always the best choice for all UKFs, or if it is only a popular choice because people do not know about those other advantages.
The difference between CHOL and some other functions that compute square roots of matrices is that CHOL is somewhat faster than most of them, typically by a factor ~ 2 or 3. However, some of the others (QR, SVD, EVD) have other advantages, such as orthogonal columns. So I do not know if CHOL is always the best choice for all UKFs, or if it is only a popular choice because people do not know about those other advantages.
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