Abstract
The equation v = q + Mv, where M is a matrix with nonnegative elements and spectral radius less than one, arises in Markovian decision processes and input-output models. In this paper, we solve the equation using an iterative aggregation-disaggregation procedure that alternates between solving an aggregated problem and disaggregating the variables, one block at a time, in terms of the aggregate variables of the other blocks. The disaggregated variables are then used to guide the choice of weights in the subsequent aggregation. Computational experiments on randomly generated and inventory problems indicate that this algorithm is significantly faster than successive approximations when the spectral radius of M is near one, and is slower in unstructured problems with spectral radii in the neighborhood of 0.8. The algorithm appears promising for large structured problems, where it can often reduce computational time and main memory storage requirements and offer greater robustness to initial values.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
