One point quadrature rule with cardinal B-spline (Q1034564)

To compute approximately an integral \(\int^m_0\varphi_m(x) f(x)\,dx\), where \(\varphi_m(\cdot)\) is a cardinal B-spline the author uses a composite rectangular rule. He proves that, on the ``quasi uniform'' mesh, the used formula has, conditionally speaking, algebraic degree of exactness \(m-1\). Under additional assumptions, the algebraic degree of exactness is \(m\).