mpt_scale_matrix

Purpose

Scales matrix row-wise and column-wise

Syntax

[An,D1,D2] = mpt_scale_matrix(A)

Description

Scales matrix ../../../fig/mpt/utils/mpt_scale_matrix1.png by finding diagonal matrices ../../../fig/mpt/utils/mpt_scale_matrix2.png and ../../../fig/mpt/utils/mpt_scale_matrix3.png in ../../../fig/mpt/utils/mpt_scale_matrix4.png such that infinity norm of each row and column approaches 1. The problem is given as

../../../fig/mpt/utils/mpt_scale_matrix15.png

Scaling matrix is used in solving linear equations of the type ../../../fig/mpt/utils/mpt_scale_matrix5.png for badly scaled matrix ../../../fig/mpt/utils/mpt_scale_matrix6.png as follows:

../../../fig/mpt/utils/mpt_scale_matrix16.png

First solve ../../../fig/mpt/utils/mpt_scale_matrix7.png, then obtain ../../../fig/mpt/utils/mpt_scale_matrix8.png.

Input Arguments

A

Input matrix do be scaled. The matrix can be also rectangular.

Class: double

Output Arguments

An

Scaled matrix ../../../fig/mpt/utils/mpt_scale_matrix9.png such that ../../../fig/mpt/utils/mpt_scale_matrix10.png.

Class: double

D1

Diagonal matrix ../../../fig/mpt/utils/mpt_scale_matrix11.png such that ../../../fig/mpt/utils/mpt_scale_matrix12.png.

Class: double

D2

Diagonal matrix ../../../fig/mpt/utils/mpt_scale_matrix13.png such that ../../../fig/mpt/utils/mpt_scale_matrix14.png.

Class: double

References

[1] Details of the method are in file drRAL2001034.ps.gz

[2] http://www.numerical.rl.ac.uk/reports/reports.html

See Also

mptopt, mpt_solve


© 2010-2013 Martin Herceg: ETH Zurich, herceg@control.ee.ethz.ch