solve A*X=B containing very large or small elements
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
hosein Javan
am 9 Aug. 2020
Kommentiert: Bruno Luong
am 10 Aug. 2020
hello
i have this linear system of equations A*X=B, which is apparently ill-conditioned with RCOND = 0. the elements in these matrices are either extremely large or small which have been derived using "besseli" and "besselk" functions.
A=
2.7673e+84 -2.7673e+84 -9.1252e-88 0 0 0 0 0 0 0
1.1039e+87 -2.2078e+90 7.2433e-82 0 0 0 0 0 0 0
0 7.7866e+105 2.5944e-109 -7.7866e+105 -2.5944e-109 0 0 0 0 0
0 6.2089e+111 -2.0604e-103 -6.2089e+111 2.0604e-103 0 0 0 0 0
0 0 0 1.5218e+110 1.2764e-113 -1.5218e+110 -1.2764e-113 0 0 0
0 0 0 1.2134e+116 -1.0138e-107 -1.2134e+116 1.0138e-107 0 0 0
0 0 0 0 0 2.2359e+127 7.5295e-131 -2.2359e+127 -7.5295e-131 0
0 0 0 0 0 1.7822e+133 -5.9817e-125 -8.9112e+129 2.9909e-128 0
0 0 0 0 0 0 0 1.9154e+170 6.5919e-174 -6.5919e-174
0 0 0 0 0 0 0 7.6309e+172 -2.6195e-171 5.239e-168
B=
-5.3706e+78
-4.2847e+84
1.5112e+100
1.205e+106
0
0
0
0
0
0
the solution is returend using X=A\B :
X=
0
1.9407e-06
4.6374e+150
8.1617e-89
4.6374e+150
1.5549e-107
4.6374e+150
-3.1817e-193
9.2546e+150
9.2616e+147
but it has realy large error:
A*X-B=
-8.2275e+63
0
-1.9427e+84
0
1.8889e+22
0
0
-1.0771e+10
-2.25e-39
0
also I am uncertained that in the future I might need to calculate other matrices which could probably contain even larger or smaller values that leads to "inf" or "0" elements.
I know that using "digits" and "vpa" functions in symbolic math toolbox it is really accurate but SPEED plays an important role in my code.
I have searched about "Fixed-point Designer Tollbox" but I did not find an example like mine.
what is the best workaround in this condition?
0 Kommentare
Akzeptierte Antwort
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Linear Algebra finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!