Before revision:  In this paper, we propose a unified way to analyze the convergence via directly studying the error of the algorithm and using the stability of the time integrator. Our analysis works for all^+ with \sigma(A) being the spectrum of A\inC^{m\times m}.
After revision:  In this paper, we propose a unified convergence analysis for the algorithm applied to u'+Au=f, where \sigma(A)\subset\mathbb{C^+ with \sigma(A) being the spectrum of A\inC^{m\times m}.