Titlebook: Symbolic Algebraic Methods and Verification Methods; Götz Alefeld,Jiří Rohn,Tetsuro Yamamoto Conference proceedings 2001 Springer-Verlag W

ACME

步兵

Matrix Methods for Solving Algebraic Systems,ications. This article surveys efficient methods based on the sparse resultant for computing all . solutions of an arbitrary system of . polynomials in . unknowns. In particular, we construct matrix formulae which yield nontrivial multiples of the resultant thus reducing root-finding to the eigendecomposition of a square matrix.

Memorial

一致性

transplantation

Derivative-Based Subdivision in Multi-Dimensional Verified Gaussian Quadrature,ify several of these control parameters and, based on experimental data, we try to give advice for choosing suitable parameter values in order to obtain reasonable average performance for a “black-box” quadrature routine.

玉米棒子

On the Shape of the Fixed Points of [f]([x]) = [A] [x] + ,thods - particularly when . is a large sparse matrix. Probably the most elementary iterative method can be derived from the socalled Richardson splitting . = . - . of ., where . is the identity matrix and . := . - .. This splitting induces the equivalent fixed point formulation . = . + . of (1) which leads to the iterative method .. = .. + ..

Mnemonics

Introduction,The usual “implementation” of real numbers as floating point numbers on existing computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly.

内阁

Expurgate

胶状

A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure,Let . = (..) ∈ ||R.... be an ., i.e. each entry is a compact real interval. ‘Usual’ matrices . ∈ |R.. with real coefficients will be called . in this paper, and a similar notation and terminology is adopted for vectors. Let . ∈ ||R.. be an interval vector. We are interested in computing an interval vector containing the solution set