Uniform convergence for cauchy principal value integrals of modified quasi-interpolatory splines^∗

^∗ Work sponsored by “Ministero dell'Università e della Ricerca Scientifica” and “Consiglio Nazionale delle Ricerche” of Italy.

Abstract

A sequence of modified quasi-interpolatory splines is introduced for numerical evaluation of Cauchy principal value integrals. Uniform convergence is proved, for a sequence of locally uniform partitions of the integration interval.

Keywords:

• Numerical evaluation of Cauchy principal value integrals
• modified quasi-interpolatory spline
• locally uniform partitions
• uniform convergence

^∗ Work sponsored by “Ministero dell'Università e della Ricerca Scientifica” and “Consiglio Nazionale delle Ricerche” of Italy.

^∗ Work sponsored by “Ministero dell'Università e della Ricerca Scientifica” and “Consiglio Nazionale delle Ricerche” of Italy.

Notes

^∗ Work sponsored by “Ministero dell'Università e della Ricerca Scientifica” and “Consiglio Nazionale delle Ricerche” of Italy.