Recently I met a problem both in Lapack and Matlab.
When I use DGEES() in Lapack or schur() in Matlab to schur_factorize a
matrix A, i.e. to make it in this form A=U*T*U'.
When I got U and T, I try to verify whether it satisfy
((Temp=A-U*T*U')==0).
The result is very disappointing.
some elements in matrix temp are several magnitude larger than elements in matrix A at corresponding positions.
What's the reason of this problem?
How to solve it?
A is 15x15 matrix ranging very wide.
0.2316733D-11 0.0000000D+00 0.1060792D-16 -0.1060792D-16 -0.1364627D-21 0.1060805D-16 0.0000000D+00 0.0000000D+00 -0.1060792D-16 0.0000000D+00 0.1364627D-21 -0.1364627D-21 -0.1878819D-42 0.0000000D+00 0.0000000D+00
0.4163336D-16 0.0000000D+00 0.1588187D-21 -0.1588187D-21 -0.1615587D-26 0.1588187D-21 0.0000000D+00 0.0000000D+00 -0.1588187D-21 0.0000000D+00 0.1615587D-26 -0.1615587D-26 -0.6842278D-48 0.0000000D+00 0.0000000D+00
0.3641793D-07 0.0000000D+00 0.1690943D-12 -0.1690943D-12 0.2605464D-19 0.1690942D-12 0.0000000D+00 0.0000000D+00 -0.1690943D-12 0.0000000D+00 -0.2605464D-19 0.2605464D-19 -0.1248483D-38 0.0000000D+00 0.0000000D+00
-0.4397242D+12 0.0000000D+00 0.1892094D-10 0.2208738D+07 -0.6233284D+00 0.2190697D+07 -0.6233284D+00 0.0000000D+00 -0.2190696D+07 0.0000000D+00 0.1804122D+05 0.2605464D-19 -0.1804122D+05 0.0000000D+00 0.0000000D+00
-0.2410358D+13 0.0000000D+00 0.7539664D+02 -0.7539664D+02 0.4717222D+07 0.3046213D-11 -0.7539664D+02 0.0000000D+00 0.2575040D-14 0.0000000D+00 0.4717146D+07 -0.4717146D+07 0.1901244D-40 0.0000000D+00 0.0000000D+00
0.2423797D-08 0.0000000D+00 0.1372268D-13 -0.1372268D-13 -0.1388481D-18 0.1372282D-13 0.0000000D+00 0.0000000D+00 -0.1372268D-13 0.0000000D+00 0.1388481D-18 -0.1388481D-18 0.1901243D-40 0.0000000D+00 0.0000000D+00
-0.8204680D+11 0.0000000D+00 0.1045757D+05 -0.8283219D+06 0.2992852D-09 -0.2575064D-14 0.8283219D+06 -0.1045757D+05 0.2575038D-14 0.8410451D-09 0.8178643D+06 -0.8178643D+06 -0.8576857D-39 0.0000000D+00 0.0000000D+00
-0.1220541D-08 0.0000000D+00 -0.2575040D-14 0.2575040D-14 0.2605464D-19 -0.2575066D-14 -0.2056157D-29 0.2056157D-29 0.2575040D-14 0.0000000D+00 -0.2605464D-19 0.2605464D-19 0.1901242D-40 0.0000000D+00 0.0000000D+00
-0.4189072D+02 0.0000000D+00 0.5157582D-06 -0.5157583D-06 0.2605464D-19 0.2846071D-09 -0.1722371D-03 0.0000000D+00 0.1727523D-03 -0.5154675D-06 0.1722371D-03 -0.1722371D-03 -0.6160259D-11 0.0000000D+00 0.0000000D+00
0.5884200D-07 0.0000000D+00 -0.2575040D-14 0.2575040D-14 0.2605464D-19 -0.2575066D-14 -0.5843693D-12 0.0000000D+00 0.2575040D-14 0.2921846D-12 -0.2605464D-19 0.2605464D-19 0.1901244D-40 0.0000000D+00 0.0000000D+00
-0.1125002D-08 0.0000000D+00 -0.2575039D-14 0.2575039D-14 -0.6079415D-19 -0.2574979D-14 0.0000000D+00 0.0000000D+00 0.2575039D-14 0.0000000D+00 0.6079415D-19 -0.6079415D-19 -0.4436235D-40 0.0000000D+00 0.0000000D+00
-0.1351098D-08 0.0000000D+00 -0.2575039D-14 0.2575039D-14 0.2605464D-19 -0.2575066D-14 0.0000000D+00 0.0000000D+00 0.2575039D-14 0.0000000D+00 -0.2605464D-19 0.2605464D-19 0.1901243D-40 0.0000000D+00 0.0000000D+00
-0.1986585D+13 0.0000000D+00 0.9579757D-04 -0.1097734D+02 0.2605464D-19 0.1444103D+08 0.0000000D+00 0.0000000D+00 -0.1444103D+08 0.0000000D+00 -0.1444105D+08 0.2605464D-19 0.1444105D+08 -0.9579757D-04 0.0000000D+00
-0.1321972D-08 0.0000000D+00 -0.2575039D-14 0.2575039D-14 0.2605464D-19 -0.2575066D-14 0.0000000D+00 0.0000000D+00 0.2575039D-14 0.0000000D+00 -0.2605464D-19 0.2605464D-19 -0.4983222D-29 0.4983222D-29 0.0000000D+00
-0.1122824D-08 0.0000000D+00 -0.2575040D-14 0.2575040D-14 0.2605464D-19 -0.2575066D-14 0.0000000D+00 0.0000000D+00 0.2575040D-14 0.0000000D+00 -0.2605464D-19 0.2605464D-19 0.1901244D-40 0.0000000D+00 0.0000000D+00