rational interval 中文意思是什麼
rational interval
解釋
有理區間-
A rational function is continuous on any finite interval where the denominator is bounded away from zero.
有理函數在任何有限區間上都是連續的，其中分母遠離零值。 -
Secondly, as for degree reduction of interval rational bezier curves, two methods are given : pseudo linear programming method ( plpm ) and pseudo optimal approximation method ( poam )
接下來對區間有理bezier曲線，給出兩種降階逼近演算法：擬線性規劃法（ plpm ）和擬最優逼近法（ poam ） 。 -
Based on the representation of interval rational bezier curves and surfaces and by a serial of mathematical transformation, the degree reductions of them are converted to those of polynomials with upper bounds, then several algorithms are presented, with linear programming and optimal approximation methods. by relaxation of some constrained conditions, approximation effects of some of them are further improved
根據區間有理bezier曲線、曲面的特點，通過一系列數學變換，將其降階問題轉化為多項式的保上界降階逼近，再應用線性規劃和最優逼近方法求解，給出幾種逼近演算法，並探討通過約束不等式的鬆弛，進一步改進逼近效果。 -
In the third chapter, interval polynomial approximation of rational curves is introduced
第三章主要介紹了有理曲線的區間多項式逼近。 -
In this paper, we survey the development of polynomial approximation of rational curves ( surfaces ) and state the knowledge of interval curves ( surfaces ) in the first chapter
本論文中，第一章首先介紹了有理曲線曲面的多項式逼近研究工作的發展情況和區間曲線曲面一些相關知識。 -
Two methods are given. one is obtained by using degree reduction of interval rational bezier curves in two parameter directions according to the character of tensor product, which is called " single step method ". by comparison for degree reductions produced by the different order in two parameter directions, the relationships of the approximation results are discussed
然後討論了矩形域上區間有理bezier曲面的降階問題，給出兩種降階演算法：一個是針對張量積的特點將問題轉變為兩參數方向的區間有理曲線的降階逼近，即「單步法」 ，並討論單步法沿兩參數方向不同次序降階的關系。 -
In the final chapter, we discuss interval polynomial approximation of rational surfaces. firstly, we briefly state the interval - surface approximation based on the taylor expansion, and later, we give out a better interval - surface approximation based on the optimization method, which is also the main work of this paper
第四章主要介紹了有理曲面的區間多項式的逼近，首先簡單介紹了基於泰勒展開來做的區間曲面逼近，後面是本文的主要工作，我們基於優化方法得到了更好的區間曲面逼近，它也是本文的重要部分。 -
It is a fast approach course adopting varied interval. collision prediction analysis is predictive course, in the course of prediction analysis there are some parameters which were selected. those parameters affect some property of prediction result certainly, including dependability veracity of prediction information and speediness of prediction, therefore they are selected rational and correctly
碰撞預警分析是一個預測過程，預警分析過程中必然涉及到一些參量的選取，主要是一些距離、時間預留量，這些參量大小的取值勢必影響到預警結果的相關屬性，包括預警信息的可靠性、準確性以及預警的快速性等，它們的選取必須是合理的和恰當的。 -
This algorithm is an extension of real root isolation algorithm for univarioie rational polynomial. it results in an higher - dimensional isolated interval for each isolated real root. in the ordinary differential equation qualitative or stability analysis, lienard systems are typical
Li nard系統是常微分方程定性及穩定性分析研究中一類典型的系統，它不僅在應用領域有著廣泛的運用，在其他微分系統的定性及穩定性分析研究中，也經常會藉助到它豐富的結論。 -
With the first method, multi - degree reduction can be executed at one time and certain continuity conditions can be satisfied ; by relaxation of constrained conditions, great improvement on the lpm of literature [ 30 ] can be obtained when interval rational bezier curves are degenerated to interval bezier curves. explicit computation formulas are presented when only one or two degrees reductions are required in the second method, and upper bounds for their errors are estimated
前者可一次性降多階，且能滿足一定的連續性要求，通過約束條件的放鬆，本文的演算法較文獻[ 30 ]的lpm法有更好的逼近；後者則給出了降一、二階時的顯式計算公式和誤差上界估計式，且逼近精度比前者更高。 -
Finally, degree reduction of interval rational triangular b - b surfaces is discussed. the problem is also converted to degree reduction of bi - variable polynomials with upper bound. according to degenerating conditions of triangular b - b surfaces, an optimization model is constructed and optimal solutions under certain constrains are calculated
先將該問題轉化為雙變量多項式的限制上界的降階問題，然後採用最優化方法，結合三角b - b曲面的退化條件，建立約束優化模型，求出約束意義下的最優解。 -
Degree reductions of interval rational bezier curves and surfaces are studied in this thesis
本文研究區間有理bezier曲線、曲面的降階逼近。
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