DETERMINING ILL CONDITIONING IN SQUARE LINEAR SYSTEM OF EQUATIONS

• US 20110270589A1
• Filed: 04/30/2010
• Published: 11/03/2011
• Est. Priority Date: 04/30/2010
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Klotz, Edward Seymour, Danna, Emilie Jeanne Anne
• Granted Patent: US 8,712,738 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 17/12 Simultaneous equations , e.g. systems of linear equations

Abstract

Determining ill conditioning in square linear systems of equations is disclosed. Specifically, a method, system and computer program product for determining ill conditioning in square linear systems of equations is disclosed, the method including sampling condition numbers in the square linear systems of equations, and classifying the condition numbers sampled from the square linear systems of equations.

Claims

1. A method for determining ill conditioning in square linear systems of equations, the method comprising:

sampling condition numbers in the square linear systems of equations; and

classifying the condition numbers sampled from the square linear systems of equations.

2. The method according to claim 1, further comprising:

generating statistics information on the square linear systems of equations according to the classifying.

3. The method according to claim 2, further comprising:

assessing a likelihood of ill conditioning according to the generated statistics information.

4. The method according to claim 1, wherein the classifying the condition numbers comprises:

obtaining a machine precision value of a computer;

obtaining a tolerance value of an application operating on the computer; and

calculating a threshold value which distinguishes large and small condition numbers according to the machine precision value of the computer and the tolerance value of an application.

5. The method according to claim 1, wherein the classifying comprises grouping the condition numbers in different categories according to a level of ill conditioning.

6. The method according to claim 5, wherein the level of ill conditioning comprises one of a stable category, a suspicious category, an unstable category and an ill-posed category.

7. The method according to claim 4, wherein if the condition number is greater than or equal to the threshold value, the square linear system is identified as ill conditioned.

8. The method according to claim 4, wherein if the condition number is less than the threshold value, the square linear system is identified as unlikely to be ill conditioned.

9. The method according to claim 1, wherein the sampling is obtained for a predetermined amount of condition numbers.

25. The method according to claim 1, further comprising:

displaying the classification of the condition numbers on a display.

10. A computer readable medium storing instructions for determining ill conditioning in linear systems of equations, the instructions comprising:

sampling condition numbers in the square linear systems of equations; and

classifying the condition numbers sampled from the square linear systems of equations.

11. The computer readable medium according to claim 10, wherein the classifying the condition numbers comprises:

obtaining a machine precision value of a computer;

obtaining a tolerance value of an application operating on the computer; and

calculating a threshold value which distinguishes large and small condition numbers according to the machine precision value of the computer and the tolerance value of an application.

12. The computer readable medium according to claim 10, wherein the classifying comprises grouping the condition numbers in different categories according to a level of ill conditioning.

13. The computer readable medium according to claim 12, wherein the level of ill conditioning comprises one of a stable category, a suspicious category, an unstable category and an ill-posed category.

14. The computer readable medium according to claim 11, wherein if the condition number is greater than or equal to the threshold value, the square linear system from which the condition number was computed is identified as ill conditioned.

15. The computer readable medium according to claim 11, wherein if the condition number is less than the threshold value, the square linear system from which the condition number was computed is identified as unlikely to be ill conditioned.

16. The computer readable medium according to claim 10, wherein the sampling is obtained for a predetermined amount of condition numbers.

17. A system for determining ill conditioning in linear systems of equations, the system comprising:

a sampling unit which samples condition numbers in the square linear systems of equations; and

a classifying unit which classifies the condition numbers sampled from the square linear systems of equations.

18. The system according to claim 17, further comprising:

a statistical analysis unit which generates statistics information on the square linear systems of equations according to the classifying in the classifying unit.

19. The system according to claim 18, further comprising:

an assessment unit which assesses a likelihood of ill conditioning according to the generated statistics information.

20. The system according to claim 17, wherein the classifying unit classifies the condition numbers by:

obtaining a machine precision value of a computer;

obtaining a tolerance value of an application operating on the computer; and

calculating a threshold value which distinguishes large and small condition numbers according to the machine precision value of the computer and the tolerance value of an application.

21. The system according to claim 17, wherein the classifying unit classifies the condition numbers by grouping the condition numbers in different categories according to a level of ill conditioning.

22. A method for determining ill conditioning in a plurality of linear systems of equations, the method comprising:

sampling a predetermined amount of condition numbers in the plurality of the square linear systems of equations;

classifying the condition numbers sampled from the plurality of square linear systems of equations according to a level of categorization;

generating statistics information on each of the plurality of square linear systems of equations according to the level of categorization; and

assessing a likelihood of ill conditioning according to the generated statistics information.

23. A method for determining ill conditioning in a square linear system of equations, the method comprising:

obtaining a condition number of the square linear system of equations; and

assessing whether the square linear system is ill conditioned according to a level of categorization of the condition number.

24. The method according to claim 23, wherein the level of categorization comprises one of a stable category, a suspicious category, an unstable category, and an ill-posed category.