Block-diagonal Schur factorization - MATLAB bdschur - 万博1manbetx,s manbetx 845,万博尤文图斯

Syntax

[T,B,BLKS] = bdschur(A,CONDMAX) [T,B] = bdschur(A,[],BLKS)

Description

[T,B,BLKS] = bdschur(A,CONDMAX)computes a transformation matrixTsuch thatB=T\A*Tis block diagonal and each diagonal block is a quasi upper-triangular Schur matrix.

[T,B] = bdschur(A,[],BLKS)pre-specifies the desired block sizes. The input matrix A should already be in Schur form when you use this syntax.

Input Arguments

A: Matrix for block-diagonal Schur factorization.
CONDMAX条件数:指定一个上界ofT. By default,CONDMAX = 1e4. UseCONDMAXto control the tradeoff between block size and conditioning ofTwith respect to inversion. WhenCONDMAXis a larger value, the blocks are smaller andTbecomes more ill-conditioned.

Output Arguments

T: Transformation matrix.
B: MatrixB=T\A*T.
BLKS: Vector of block sizes.

Version History

Introduced in R2008a

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R2022a: Default value of`CONDMAX`input argument changed

Behavior changed in R2022a

The default value ofCONDMAXinput argument is now1e4. Previously, the default value was1/sqrt(eps). IncreasingCONDMAXreduces the size of the eigenvalue clusters in the transformed model but also decreases the accuracy of the transformation. The new default value balances the conditioning and transformation accuracy. If you have code that relies on the default value ofCONDMAXbeing1/sqrt(eps), update your code to explicitly set this input argument.

bdschur