Matrices, Moments, and Rational Quadrature Articles uri icon

publication date

  • November 2008

start page

  • 2540

end page

  • 2554

issue

  • 10

volume

  • 429

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856

abstract

  • Many problems in science and engineering require the evaluation of functionals of the form Fu(A)=uTf(A)u, where A is a large symmetric matrix, u a vector, and f a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to A with initial vector u, and then evaluating pairs of Gauss and Gauss&-Radau quadrature rules associated with the tridiagonal matrix determined by the Lanczos procedure. The present paper extends this approach to allow the use of rational Gauss quadrature rules.