72 research outputs found
On the convergence of the quadratic method
The convergence of the so-called quadratic method for computing eigenvalue
enclosures of general self-adjoint operators is examined. Explicit asymptotic
bounds for convergence to isolated eigenvalues are found. These bounds turn out
to improve significantly upon those determined in previous investigations. The
theory is illustrated by means of several numerical experiments performed on
particularly simple benchmark models of one-dimensional Schrodinger operators.Comment: Main result extended to isolated eigenvalues of general self-adjoint
operators. Two gaps in proofs and many typos correcte
Generalised cosine functions, basis and regularity properties
We examine regularity and basis properties of the family of rescaled
-cosine functions. We find sharp estimates for their Fourier coefficients.
We then determine two thresholds, , such that this family is
a Schauder basis of for all and .Comment: 24 page
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