## Abstract

The problem of finding the global minimum of a so-called Minkowski-norm dominated polynomial can be approached by the matrix method of Stetter and Mo'ller, which reformulates it as a large eigenvalue problem. A drawback of this approach is that the matrix involved is usually very large. However, all that is

needed for modern iterative eigenproblem solvers is a routine which computes the action of the matrix on a given vector. This paper focuses on improving the efficiency of computing the action of the matrix on a vector. To avoid building the large matrix one can associate the system of first-order conditions with an

nD system of difference equations. One way to compute the action of the matrix efficiently is by setting up a corresponding shortest path problem and solving it. It turns out that for large n the shortest path problem has a high computational complexity, and therefore some heuristic procedures are developed for arriving

cheaply at suboptimal paths with acceptable performance.

needed for modern iterative eigenproblem solvers is a routine which computes the action of the matrix on a given vector. This paper focuses on improving the efficiency of computing the action of the matrix on a vector. To avoid building the large matrix one can associate the system of first-order conditions with an

nD system of difference equations. One way to compute the action of the matrix efficiently is by setting up a corresponding shortest path problem and solving it. It turns out that for large n the shortest path problem has a high computational complexity, and therefore some heuristic procedures are developed for arriving

cheaply at suboptimal paths with acceptable performance.

Original language | English |
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Pages (from-to) | 30-53 |

Number of pages | 24 |

Journal | Journal of Symbolic Computation |

Volume | 42 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Jan 2007 |