Pseudospectra of Linear Operators

If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ||An|| or ||exp(tA)||. More may be learned by examining the sets in the complex plane known as the pseudospectra of A, defined by level curves of the norm of the resolvent, ||(zI - A)-1||. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles.

• Publication year

  1997

• Venue

  SIAM Review

• Publication date

  1997-09-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1137/S0036144595295284
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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