الملخص
For iterative solution of symmetric systems the conjugate gradient method (CG) is commonly used when A is positive definite, while the minimum residual method (MINRES) is typically reserved for indefinite systems. We investigate the sequence of approximate solutions generated by each method and suggest that even if A is positive definite, MINRES may be preferable to CG if iterations are to be terminated early. In particular, we show for MINRES that the solution norms are monotonically increasing when A is positive definite (as was already known for CG), and the solution errors are monotonically decreasing. We also show that the backward errors for the MINRES iterates are monotonically decreasing.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.24200/squjs.vol17iss1pp44-62
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 16, 44
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY 4.0
اقتبس هذه المقالة
APA 7
Fong, D. C. L., & Saunders, M. A. (2012). CG Versus MINRES: An Empirical Comparison. Sultan Qaboos University Journal for Science, 16, 44. https://doi.org/10.24200/squjs.vol17iss1pp44-62
MLA 9
Fong, David Chin-Lung, and Michael A. Saunders. "CG Versus MINRES: An Empirical Comparison." Sultan Qaboos University Journal for Science, vol. 16, 2012, pp. 44. https://doi.org/10.24200/squjs.vol17iss1pp44-62.
شيكاغو (المؤلف–التاريخ)
Fong, David Chin-Lung, and Michael A. Saunders. 2012. "CG Versus MINRES: An Empirical Comparison." Sultan Qaboos University Journal for Science 16: 44. https://doi.org/10.24200/squjs.vol17iss1pp44-62.
هارفارد
Fong, D. C. L. and Saunders, M. A. (2012) 'CG Versus MINRES: An Empirical Comparison', Sultan Qaboos University Journal for Science, 16, pp. 44. doi:10.24200/squjs.vol17iss1pp44-62.
فانكوفر
Fong DCL, Saunders MA. CG Versus MINRES: An Empirical Comparison. Sultan Qaboos University Journal for Science. 2012;16:44. doi:10.24200/squjs.vol17iss1pp44-62
IEEE
D. C. L. Fong, and M. A. Saunders, "CG Versus MINRES: An Empirical Comparison," Sultan Qaboos University Journal for Science, vol. 16, pp. 44, 2012, doi: 10.24200/squjs.vol17iss1pp44-62.