ACTUAL FACTOR DECISION METHOD AND REAL FACTOR DECISION DEVICE FOR REAL INTERVAL POLYNOMIAL, REAL FACTOR DECISION PROGRAM AND RECORDING MEDIUM

摘要

PROBLEM TO BE SOLVED: To decide whether a real interval polynomial has a real coefficient polynomial as a real factor or not.;SOLUTION: The real interval polynomial Σ[l_i, h_i]e_i(x) is divided by the real coefficient polynomial f in each e_i(x) to obtain a residue r_i(x). When a number satisfying l_i=h_i is present, the residues to them are added to generate r₀(x). By removing the residual satisfying r_i(x)=0, the real interval polynomial r₀(x)+Σ[l_i, h_i]r_i(x) is generated. An interval width of each interval coefficient of the generated real interval polynomial is normalized to a unit length, and is rewritten to p₀(x)+Σ[0, 1]p_i(x), and the real interval polynomial is regarded as a convex polyhedron. Affine mapping that is surjective to the convex polyhedron is performed from a hypercube. When a plane mapped by the affine mapping among planes of the hypercube becomes a facet of the convex polyhedron, a hyper plane including the facet and a hyperplane parallel to the hyperplane, including another facet parallel to the facet are obtained. By deciding whether a point 0 exists between the two hyperplanes or not, it is decided whether the real interval polynomial has the real factor or not.;COPYRIGHT: (C)2009,JPO&INPIT