The geometrical meaning of the Kantorovich–Wielandt inequalities

✍ Scribed by Karl Gustafson

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 92 KB
• Volume: 296
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00106-8

✦ Synopsis

The Kantorovich±Wielandt angle he and the author's operator angle /e are related by cos /e 2 sin he. Here A is an arbitrary symmetric positive de®nite (SPD) matrix. The relationship of these two dierent geometrical perspectives is discussed. An extension to arbitrary nonsingular matrices A is given. A related four-way relationship with the operator trigonometry, strengthened CBS constants, and domain decomposition methods is noted.