Linear algebra

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balance

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Diagonal scaling to improve eigenvalue accuracy.

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Syntax

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B = balance(A)

B = balance(A,'noperm')

[T, B] = balance(A)

[S, P, B] = balance(A)

Input argument

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A

a matrix: square, finite single or double.

Output argument

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B

balanced matrix.

T

similarity transformation: Rearrange the elements of a diagonal matrix containing integer powers of two in order to minimize the impact of roundoff errors.

S

scaling vector

P

permutation vector

Description

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B = balance(A) returns the balanced matrix B.

B = balance(A, 'noperm') scales A without permuting its rows and columns.

Used function(s)

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LAPACKE_dgebal, LAPACKE_sgebal, LAPACKE_zgebal, LAPACKE_cgebal

Example

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A = [10  1000  100000; .1  10  1000; .001  .1  10]
F = balance(A)

See also

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eig.

History

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Version	Description
1.0.0	initial version

Author

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Allan CORNET