Universal algorithms for solving the matrix Bellman equations over semirings
نویسندگان
چکیده
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed.
منابع مشابه
Universal algorithms for generalized discrete matrix Bellman equations with symmetric Toeplitz matrix
This paper presents two universal algorithms for generalized discrete matrix Bellman equations with symmetric Toeplitz matrix. The algorithms are semiring extensions of two well-known methods solving Toeplitz systems in the ordinary linear algebra.
متن کاملUnified Algorithm to Solve Several Graph Problems with Relational Queries
Several important graph algorithms can be solved as an iteration of vector-matrix multiplication over different semirings. On this basis, we show that the Bellman-Ford (single source shortest paths), reachability, PageRank, and topological sort algorithms can be expressed as relational queries, to solve analytic graph problems in relational databases. As a main contribution, we present a genera...
متن کاملSolving Linear Systems on Linear Processor Arrays Using a ∗-Semiring Based Algorithm
∗-semirings are algebraic structures that provide a unified approach to solve several problem classes in computer science and operations research. Matrix computations over ∗-semirings are interesting because of their potential applications to linear algebra. In this paper, we present a parallel algorithm for solving systems of linear equations on ∗-semirings using linear arrays. Most of the wor...
متن کاملFinite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...
متن کاملOn the numerical solution of generalized Sylvester matrix equations
The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection metho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Soft Comput.
دوره 17 شماره
صفحات -
تاریخ انتشار 2013