A new algorithm for a recursive construction of the minimal interpolation space

In this work, we introduce a new interpolation algorithm, based on a recursive method for computing Lagrange interpolants. This algorithm allows to construct recursively the minimal interpolation space (see [1]) with respect to a finite set of points. We also extend this recursive method to the osculatory interpolation problem.     

A recursive method for solving unconstrained tangentialinterpolation problems

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recursive procedure admits a physical interpretation in terms of discretized transmission lines. In this framework the generating system is constructed as a cascade of first-order sections. Singular steps occur only when the input data is contradictory, i.e., only when the interpolation problem does not have a solution. Various pivoting schemes can be used to improve numerical accuracy or to impose additional constraints on the interpolants. The algorithm also provides coprime factorizations for all rational interpolants and can be used to solve polynomial interpolation problems such as the general Hermite matrix interpolation problem. A recursive method is proposed to compute a column-reduced generating system that can be used to solve the minimal tangential interpolation problem     

Time-variant displacement structure and interpolation problems

Derives a new recursive solution for a general time-variant interpolation problem of the Hermite-Fejer type, based on a fast algorithm for the recursive triangular factorization of time-variant structured matrices. The solution follows from studying the properties of an associated cascade system and leads to a triangular array implementation of the recursive algorithm. The system can be drawn as a cascade of first-order lattice sections, where each section is composed of a rotation matrix followed by a storage element and a tapped-delay filter. Such cascades always have certain blocking properties, which can be made equivalent to the interpolation conditions. The authors also illustrate the application of the algorithm to problems in adaptive filtering, model validation, robust control, and analytic interpolation theory     

Reversible video watermarking through recursive histogram modification

In this study, a new reversible video watermarking method is developed. Unlike the existing reversible video watermarking algorithms that are based on motion compensated prediction or interpolation error expansion, motion compensated interpolation errors in the proposed method are watermarked in a totally different manner with the aid of recursive histogram modification algorithm developed recently for the purpose of reversible image watermarking. However,the recursive histogram modification can not be used directly for reversible video watermarking since the important problems of ensuring reversibility for each frame and distribution of total capacity among frames are encountered. In this study, novel ideas are proposed to solve the aforementioned two problems. The proposed method is tested on the video sequences commonly used in the literature. It is shown to give better performance than the existing reversible video watermarking algorithms in terms of capacity and distortion by means of computer simulations. Also, a numerical example is provided.     

基于递归插值与逼近的曲面拟合改进算法

对原有的递归插值分割曲面算法进行了分析,给出了基于递归插值与逼近的曲面拟合改进算法,克服了原有算法在复杂曲面拟合中由于已知点分布不均匀等因素造成的困难,改善了曲面拟合的效果和效率。     

混合插值法重构近地表模型

当控制点多和网格稠密时,基于薄板样条(TPS)插值的近地表模型重构往往很耗时,影响了静校正中近地表建模的效率.针对此问题,采用一种TPS插值和三次样条插值相结合的混合插值法重构近地表模型.首先利用矩阵递归LU分解及GPU加速的LU分解算法求解大型线性方程组,建立TPS插值函数;然后在X和Y方向上使用适当的步长对网格进行抽稀,运用TPS插值函数计算稀疏网格点的值,再通过稀疏网格点建立三次样条插值函数并计算剩余网格点的值;最后用OpenGL实现近地表模型的三维可视化.实验结果表明,文中算法提高了近地表模型重构的速度,其精度接近TPS插值精度.     

Spatial?temporal content-adaptive deinterlacing algorithm

An algorithm, which adapts to an appropriate interpolation technique for high-quality deinterlacing based on the spatial?temporal spectral and edge-oriented features of local video contents, is introduced. This algorithm employs a spectrum-adaptive vertical?temporal filter to deal with generic video scenes, and adopts a texture-adaptive edge-based line-averaging interpolation with an edge-consistency check to interpolate moving edges with high efficiency. This deinterlacing algorithm likewise incorporates an economical recursive stationary-pixel detection scheme with a field-averaging filter to effectively interpolate stationary video scenes. Because of the precise selection of the interpolation technique for versatile video contents, the proposed algorithm provides not only better objective peak signal-to-noise ratio, but also results in more impressive subjective visual quality when compared with other non-motion compensated deinterlacing approaches.     

四点插入生成曲线的递归算法及在分形绘图中的应用

本文讨论基于四点插入的曲线生成方法的产发实现问题，说明实现算法可以在分形绘图中得到应用，并给出了一些实例。     

时变谐波参数检测

本文以自适应线性组合器为基础,采用递归最小二乘法进行时变谐波参数的跟踪检测。当信号的基波频率发生变化时,采用分段检测的思想,对每小段信号先采用插值快速傅立叶变换法检测该段基波频率,作为自适应线性组合器的输入,然后采用递归最小二乘法进行幅度和相位的跟踪检测。该方法利用递归最小二乘法跟踪速度快的特点,实现了时变谐波的快速跟踪检测。实验结果验证了所提方法的有效性和准确性。     

A new method of mesh simplification for 3-Dimension terrain using Laplace operator

This paper proposes a new method to simplify mesh in 3D terrain.The 3D terrain is presented by digital elevation model.First,Laplace operator is introduced to calculate sharp degree of mesh point,which indicates the variation trend of the terrain.Through setting a critical value of sharp degree,feature points are selected.Second,critical mesh points are extracted by an recursive process,and constitute the simplified mesh.Third,the algorithm of linear-square interpolation is employed to restore the characteristics of the terrain.Last,the terrain is rendered with color and texture.The experimental results demonstrate that this method can compress data by 16% and the error is lower than 10%.     

满足数据点切向约束的二次B样条插值曲线

给出一种二次B样条曲线插值方法.利用数据点的参数化和节点向量的自由度,构造在各数据点满足切向约束的二次B样条插值曲线,直观地控制插值曲线达到预期形状.用文中方法构造插值曲线是一个递推过程,不必预先确定数据点参数值和节点向量、不必解线性方程组,而是在插值过程中根据数据点及其切向的约束条件递推地确定数据点的参数值、节点和控制顶点.该文方法允许插值曲线各段的连接点与数据点不一致,以使得二次B样条插值曲线的形状更自然.而且在满足数据点切向约束的条件下,还可利用节点进一步调控插值曲线的形状.另外,用文中方法构造的二次B样条插值曲线对于数据点的改变具有较好的局部性质.文中最后给出一些例子将该文方法与其它一些插值方法进行比较,实验结果表明,该文方法是有效的.     

递归算法的参数设置

递归算法参数的设置是至关重要的,基于递归算法的特征,提出一种通用的递归算法的设计模式．在此基础上进一步讨论参数的设置的方式及其效果,为研究递归算法提供有效的解决方案,具有很强的实用性,并结合经典实例给以说明。     

RGIA算法的QR分解实现

提出递推辨识算法一般形式(简称RGIA)的QR分解实现方法,并推导出相应的基 于HOUSEHOLDER变换的快速递推算法.该算法可用于各种递推辨识算法中,以减小增益 矩阵计算的误差积累和传递,提高辨识精度,同时减少了计算所需的运算量.数值仿真结果表 明该算法是正确的.     

递归算法的参数设置

递归算法参数的设置是至关重要的,基于递归算法的特征,提出一种通用的递归算法的设计模式,在此基础上进一步讨论参数的设置的方式及其效果,为研究递归算法提供有效的解决方案,具有很强的实用性,并结合经典实例给以说明。     

由遍历结果还原二叉树的递归算法

二叉树的遍历操作和其它操作的算法实现,都必须先创建二叉树。分析常规创建二叉树方法的特点和不足,给出利用中序遍历和后序遍历结果还原二叉树的算法,利用这一方法,给出由前序遍历和后序遍历还原二叉树的算法,最后,提供利用次层遍历和中序遍历还原二叉树的算法。     

基于目标函数的递推子空间辨识算法

针对实际工程中要求对系统参数进行在线估计的问题, 提出一种递推子空间辨识的新方法. 通过引入辅助变量关系将递推子空间辨识问题转化为目标函数的迭代最小化问题. 采用递推最小二乘算法在线估计参数并由传播方法得到更新的广义能观性矩阵, 进而求得子空间辨识模型系统参数. 该算法简单有效且对初值具有鲁棒性. 最后, 通过仿真实例验证算法的有效性.     

乔莱斯基分解递归算法的研究

1 引言以乔莱斯基(Cholesky)分解、LU分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用。随着计算机结构和技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展。通用的基本线性代数子程序库BLAS(Basic Lin-ear Algebra Subprograms)从70年代的Level-1 BLAS(执行向量一向量运算),发展到80年代的Level-2     

Cholesky分解递归算法与改进

递归算法是计算稠密线性代数的一种新的有效方法。递归产生自动、变化的矩阵分块,能充分发挥当今分级存储高性能计算机的效率。对Cholesky分解递归算法进行了研究,给出了算法的详细推导过程,用具有递归功能的Fortran90实现了算法,并通过矩阵元素顺序重排的方法,进一步提高了递归算法的运算速度。研究产生的算法比目前常用的分块算法快15％－25％。     

递推广义预测自校正控制器

本文给出了广义预测自校正控制器的递推算法,用递推平方根法代替最小二乘法估计参 数,改善了计算精度,比牛津大学克拉克等人的算法节省了计算时间.仿真实验表明,该控制 器对系统时延与阶次有很好的鲁棒性,性能优于PID调节器、广义最小方差自校正器与极点 配置自校正器,有较强的抑制干扰能力.     

A recursive algorithm for estimating multiple models continuous transfer function with non-uniform sampling

A multiple model recursive least squares algorithm combined with a first-order low-pass filter transformation method, named λ-transform, is proposed for the simultaneous identification of multiple model orders continuous transfer functions from non-uniformly sampled input–output data. The λ-transformation is shown to be equivalent to a canonical transformation between discrete z-domain and δ-domain using the negative value of the λ-transform filter time-constant instead of the sampling interval parameter. The proposed algorithm deals with oversampling, sampling jitter or non-uniform sample intervals without the need for extra digital anti-aliasing pre-filtering, downsampling or interpolation algorithms, producing multiple models with a cost function that facilitates automatic selection of best-fitted models. Besides, measurement noise is noted as beneficial, bringing up an inherent bias toward low-order models. Simulated examples and a drum-boiler level experimental result exhibiting non-minimum phase behaviour illustrate the application of the proposed method.