  The Landweber algorithm defined on complex/real Hilbert spaces is a gradient
descent algorithm for linear inverse problems. Our contribution is to present a
novel method for accelerating convergence of the Landweber algorithm. In this
paper, we first extend the theory of the Chebyshev inertial iteration to the
Landweber algorithm on Hilbert spaces. An upper bound on the convergence rate
clarifies the speed of global convergence of the proposed method. The Chebyshev
inertial Landweber algorithm can be applied to wide class of signal recovery
problems on a Hilbert space including deconvolution for continuous signals. The
theoretical discussion developed in this paper naturally leads to a novel
practical signal recovery algorithm. As a demonstration, a MIMO detection
algorithm based on the projected Landweber algorithm is derived. The proposed
MIMO detection algorithm achieves much smaller symbol error rate compared with
the MMSE detector.
