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Applied Analysis Errata II - Errata Applied...

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Errata Applied Analysis (Corrected in online files but not in Second Printing) p. 115: Replace statement of Theorem 5.53 with: “A consistent ap- proximation scheme is convergent if and only if it is stable.” p.115: Replace last paragraph (“Conversely...”) of the proof of The- orem 5.53 with: “Conversely, we prove that a convergent scheme is stable. For any f Y , let u = A - 1 f . Then, since the scheme is convergent, we have u u as 0, where u = A - 1 f , so that u is bounded. Thus, there exists a constant M f , independent of , such that k A - 1 f k ≤ M f . The uniform boundedness theorem, which we do not prove here, then implies that there exists a constant
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