An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal ...An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.展开更多
样条函数是函数逼近理论一个非常活跃的分支,促使了研究人员需要深刻认识样条函数的本质及性质。本文介绍了基于Hermite两点三次公式的三转角插值算法。三转角以插值节点的一阶导数为未知量构建样条函数,在此基础上,研究插值节点均匀分...样条函数是函数逼近理论一个非常活跃的分支,促使了研究人员需要深刻认识样条函数的本质及性质。本文介绍了基于Hermite两点三次公式的三转角插值算法。三转角以插值节点的一阶导数为未知量构建样条函数,在此基础上,研究插值节点均匀分布时,在第二类边界条件下,即II型插值条件下,当边界初值发生扰动时,对应的三次样条函数在插值节点的一阶导数值如何随第二边界初值的扰动而变化,基于Doolittle分解和Crout分解性质,推导出2个定理,即误差估计的表达式,这些定理为三次样条函数在二阶导数边界初值变化时的误差分析提供了可行的方法。Spline function is a very active branch of function approximation theory, which makes researchers need to deeply understand the essence and properties of spline function. This paper introduces the three-angle interpolation algorithm based on Hermite two-point cubic formula. The three-angle spline function is constructed with the first derivative of the interpolating node as an unknown quantity. On this basis, when interpolating nodes are evenly distributed, under the second type of boundary condition, that is, under the type II interpolation condition, when the initial value of the boundary is disturbed, the corresponding cubic spline function in the interpolating node’s first derivative value changes with the disturbance of the initial value of the second boundary. Based on the properties of Doolittle decomposition and Crout decomposition, two theorems, namely the expression of error estimation, are derived. These theorems provide a feasible method for error analysis of cubic spline function when the initial value of the second derivative boundary changes.展开更多
"We were given their finest accom-modations since we were the Americans who had just bombed Japan.The extra clothing was like cardboard but it was thick and warm.The beds were way too small,but they were a welcom..."We were given their finest accom-modations since we were the Americans who had just bombed Japan.The extra clothing was like cardboard but it was thick and warm.The beds were way too small,but they were a welcome sight to us."These words were penned in a 1942 diary entry by Charles Ross Greening,an American pilot and one of the famed Doolittle Raiders.Later published in his memoir Not as Briefed,Greening's account describes his experience in Quzhou,a city nestled in the western part of China's Zhejiang Province.展开更多
On April 18,1942,in direct response to the Japanese attack on Pearl Harbor,the United States launched the Doolttle Raid mission.Led by Lieutenant Colonel James Doolittle,80 airmen took to the skies in B-25 bombers to ...On April 18,1942,in direct response to the Japanese attack on Pearl Harbor,the United States launched the Doolttle Raid mission.Led by Lieutenant Colonel James Doolittle,80 airmen took to the skies in B-25 bombers to strike Tokyo and other key Japanese cities.However,due to unforeseen circumstances,the crews failed to land at Quzhou Airport in the eastern Chinese province of Zhejiang as planned after they ran out of fuel.展开更多
基金supported by the National Natural Science Foundation of China (No. 10771030)the Key Project of Ministry of Education of China (No. 107098)+1 种基金the Specialized Research Fund for the Doc-toral Program of Higher Education of China (No. 20070614001)the Applied Basic ResearchProject of Sichuan Province (No. 2008JY0052)
文摘An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.
文摘样条函数是函数逼近理论一个非常活跃的分支,促使了研究人员需要深刻认识样条函数的本质及性质。本文介绍了基于Hermite两点三次公式的三转角插值算法。三转角以插值节点的一阶导数为未知量构建样条函数,在此基础上,研究插值节点均匀分布时,在第二类边界条件下,即II型插值条件下,当边界初值发生扰动时,对应的三次样条函数在插值节点的一阶导数值如何随第二边界初值的扰动而变化,基于Doolittle分解和Crout分解性质,推导出2个定理,即误差估计的表达式,这些定理为三次样条函数在二阶导数边界初值变化时的误差分析提供了可行的方法。Spline function is a very active branch of function approximation theory, which makes researchers need to deeply understand the essence and properties of spline function. This paper introduces the three-angle interpolation algorithm based on Hermite two-point cubic formula. The three-angle spline function is constructed with the first derivative of the interpolating node as an unknown quantity. On this basis, when interpolating nodes are evenly distributed, under the second type of boundary condition, that is, under the type II interpolation condition, when the initial value of the boundary is disturbed, the corresponding cubic spline function in the interpolating node’s first derivative value changes with the disturbance of the initial value of the second boundary. Based on the properties of Doolittle decomposition and Crout decomposition, two theorems, namely the expression of error estimation, are derived. These theorems provide a feasible method for error analysis of cubic spline function when the initial value of the second derivative boundary changes.
文摘"We were given their finest accom-modations since we were the Americans who had just bombed Japan.The extra clothing was like cardboard but it was thick and warm.The beds were way too small,but they were a welcome sight to us."These words were penned in a 1942 diary entry by Charles Ross Greening,an American pilot and one of the famed Doolittle Raiders.Later published in his memoir Not as Briefed,Greening's account describes his experience in Quzhou,a city nestled in the western part of China's Zhejiang Province.
文摘On April 18,1942,in direct response to the Japanese attack on Pearl Harbor,the United States launched the Doolttle Raid mission.Led by Lieutenant Colonel James Doolittle,80 airmen took to the skies in B-25 bombers to strike Tokyo and other key Japanese cities.However,due to unforeseen circumstances,the crews failed to land at Quzhou Airport in the eastern Chinese province of Zhejiang as planned after they ran out of fuel.
