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This is the so-called Duerlite algorithms: from the bottom row of the matrix A do elementary transformation, the diagonal elements into the bottom left of zero, and then show the effect of these lines is equivalent to transform the left by a unit lower triangular matrix, this series of unit lower triangular matrix inverse is the product of L matrices, it is also a unit lower triangular matrix.

这正是所谓的杜尔里特算法:从下至上地对矩阵A做初等行变换,将对角线左下方的元素变成零,然后再证明这些行变换的效果等同于左乘一系列单位下三角矩阵,这一系列单位下三角矩阵的乘积的逆就是L矩阵,它也是一个单位下三角矩阵。

In Chapter 4, a symmetric triangular partitioned secant method for solving large scale sparse unconstrained optimization problems is constructed, which is a combination of a secant method and a finite difference method, and depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix; it reduces the number of gradient evaluations required by Powell and Toints algorithm (the indirect lower triangular substitution algorithm) by one at every iterative step.

此算法是基于稀疏Hesse阵的下三角部分的列的相容分划的基础上建立起来的,把割线法和有限差分法有机的结合在了一起,在每次迭代中,把由Powell和Toint的算法所需要的梯度赋值次数减少了一。

And three special kind of triangular decomposition is introduced. In addition, the calculation of matrix's triangular decomposition and the application on matrix's triangular decomposition are detailedly discussed.

并介绍了三类特殊矩阵的三角分解,且对矩阵三角分解的计算及应用作了较详细的论述。

Chapter 2: The principles of triangular Bezier surface modeling were introduced, including degree elevation, differentiation, split and reginal change, etc. The explicit triangular Bezier C〓 modeling and parametric triangular Bezier GC〓 modeling were also introduced.

第二章 系统研究了Bezier三角曲面的基本理论,包括Bezier三角曲面的升阶、求导、分割和区域变换理论;给出了显式Bezier三角曲面的C〓构造和参数Bezier三角曲面的GC〓构造方法。

Culm sheaths deciduous, narrowly triangular-rounded, 1/2–3/5 as long as internodes, thinly leathery, radially white-gray setose, longitudinal ribs conspicuous, margins densely ciliate; auricles and oral setae absent; ligule arcuate or nearly truncate, 0.5–1 mm; blade erect, triangular to linear-triangular, width nearly equal to apex of culm sheath.

脱落,狭三角形绕行的竿箨,节间,薄革质的1/2-3/5倍于,显眼的白色灰色具刚毛,长度肋骨,纤毛的边缘密的光线;叶耳和口头的刚毛无;叶舌弧曲的或近截形,0.5-1毫米;叶片直立,三角形到线形三角形,宽度差不多等于竿箨的先端。

Leaves ovate to ovate-lanceolate, base rounded to cuneate-attenuate, margin crenate or serrate except at base.

叶卵形到卵状披针形,渐狭的基部圆形到楔形,边缘具圆齿或有锯齿除在基部之外。

Leaf blade membranous, oblong-ovate or ovate-orbicular, margin crenate to serrate; terminal bud not spinescent.

叶片膜质,长圆状卵形的或卵形圆形,对有锯齿的边缘具圆齿;顶芽不具刺。

Stems erect or decumbent; leaves ovate or lanceolate-ovate.

茎直立或外倾;卵形叶卵形的或披针形。

Leaf blade ovate to broadly ovate, apex usually caudate; endocarp smooth or ± sculptured.

叶片卵形到宽卵形,先端通常尾状;内果皮光滑或者±雕刻。

Scandent or erect shrubs; leaf blade ovate-oblong or ovate-lanceolate, broadest at lower part, apex acute or acuminate, adaxially ferruginous; drupe 5-6 mm in diam.

Scandent或者直立灌木;披针形叶片卵形长圆形或卵形,在下半部分最宽,先端锐尖或渐尖,正面铁锈色;核果5-6毫米直径 6 Z。

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