n次乘、开方去9余数验算法

求相同因数乘积的运算叫做乘方;求一个数方根的运算叫做开方。乘方与开方运算可用珠算,亦可用笔算,但运算过程比较烦琐,稍不当心就容易出错,因此答数需要检查,而检查的方式往往复算,甚至多次复算,这是非常乏味的。现介绍一种简捷的"去9余数验算法",不论是多少次乘、开方运算,只要按此法验算,     

X射线荧光分析中X射线管原级能谱分布的测定

确切知道X射线管激发的原级能谱分布是X射线荧光分析中的一个重要前提,所用能谱分布函数的准确度大大影响了最终的测量结果。提出利用间接测量法,选用合适的参量模型来描述X射线的原级能谱分布。依靠实验测得的厚靶纯元素样品的荧光强度,利用已知的理论公式,建立非线性方程,优化得到参量模型中的参量值。通过比较实验测得的元素的荧光强度值和利用得到的能谱分布函数计算的理论值,证明此种方法是可行的。     

A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS

Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting.     

Least-square Solutions of Inverse Problems for Anti-symmetric and Skew-symmetric Matrices

The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.     

试论“三算教育”与“珠算式心算教育”的关系

所谓“三算”就是笔算、珠算和口算三种计算方法。“三算教育”，就是根据三算各自的特点与长处，将三种计算方法有机地结合起来的一种初等数学的教学。而“珠算式心算”，就是在娴熟的珠算技术的基础上，珠算升华到脑算，即珠算的高级阶段。珠算在人的大脑中形成了映象——脑算盘图。计算者用自己的“脑算盘图”进行加减乘除、乘方和开方等计算。“珠算式心算教育”，是根据“脑算图”的特点与长处，用脑思维拨珠进行计算的一种比较高级的初等数学的教学。     

N次乘、开方去9余数验算表

求相同因数乘积的运算叫做乘方;求一个数方根的运算叫做开方。乘方与开方运算可用珠算、珠心算。亦可用笔算,但高次方运算过程比较烦琐,稍不当心就容易出错,因此答数需要检查,而检查的方式只有复算,甚至多次复算,这是非常乏味的。现介绍一种简捷的“去9余数验算法”,无论是多少乘方或开方运算,只要对照本文中“N次乘、开方去9余数验算表”,按此法验算,便能很快判断答数是否正确。     

Modelling of chaotic systems based on modified weighted recurrent least squares support vector machines

Positive Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially. In this paper, we propose the modified version of the support vector machines (SVM) to deal with this problem. Based on recurrent least squares support vector machines (RLS-SVM), we introduce a weighted term to the cost function tocompensate the prediction errors resulting from the positive global Lyapunov exponents. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to the Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.     

弃繁就简 返璞归真

在学习了乘方运算以后,我们很容易得到下面两个不等式:对于任意的实数a、b,都有:a2+b2≥-2ab(Ⅰ)a2+b2≥2ab(Ⅱ)     

A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES

A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems.The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.