Structured backward errors for KKT systems

✍ Scribed by Ji-guang Sun

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 867 KB
• Volume: 288
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(98)10184-2

✦ Synopsis

Karush--lZ uhn--Tucker (KKT) systems are linear system~ with coefficient rnatrices of

where H is symmetric A normwisc structured backward error for K KT systems is defined, and a computable formuht of the structured back~ard error i~ obtained. Simple examples show that the structured backward er,'or may ,~e arbitrarily klrgcr Ihan the unstructured ones in the worst case, and a stable algo..,'ithrl for solving KKT systems is not necessarily strongly stable. Consequently, the computabhr formula of the structured backward error may be uset'ul for testing the :,trong s~ability of practical algorithms h~r solving KKT systems.