bdschur

Block-diagonal Schur factorization.

📝 Syntax

• [T, B] = bdschur(A)

• [T, B] = bdschur(A, CONDMAX)

📥 Input argument

• A - Square real matrix.

• CONDMAX - upper bound on the condition number of T. By default, CONDMAX = 1e4.

📤 Output argument

• T - Transformation matrix.

• B - B = T \ A * T

📄 Description

[T, B] = bdschur(A, CONDMAX) calculates a transformation matrix T, where B = T \ A * T results in a block diagonal matrix with each block being a quasi upper-triangular Schur matrix, ensuring the diagonalization of matrix A while preserving certain structural properties.

Used function(s)

MB03RD

📚 Bibliography

http://slicot.org/objects/software/shared/doc/MB03RD.html

💡 Example

A = [1.   -1.    1.    2.    3.    1.    2.    3.;
   1.    1.    3.    4.    2.    3.    4.    2.;
   0.    0.    1.   -1.    1.    5.    4.    1.;
   0.    0.    0.    1.   -1.    3.    1.    2.;
   0.    0.    0.    1.    1.    2.    3.   -1.;
   0.    0.    0.    0.    0.    1.    5.    1.;
   0.    0.    0.    0.    0.    0.    0.99999999   -0.99999999;
   0.    0.    0.    0.    0.    0.    0.99999999    0.99999999];
[T, B] = bdschur(A)

🔗 See also

slicot_mb03rd.

🕔 History

Version	📄 Description
1.0.0	initial version