# 计算多项式

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Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

Therefore,we know that under the mean of statistics, interpolation operators are not only ideal algorithm for realizing optimal approximation polynomials computation,but also ideal computing tool for realizing optimal information- based operation,and the property of their recover functions are good.

It takes the function made up of Legendre orthogonal polynomial as displacement function, and use Galerkin method to solve this function. The methods calculating formulas is very simple, so the method can avoid the great calculating difficulty of traditional simplified methods.

Finally, we present an efficient algorithm for computing the minimal polynomial of a polynomial matrix. It determines the coefficient polynomials term by term from lower to higher degree.

Nonlinear equation of a polynomial f = 0 in solving problems, I numerical analysis courses designed to do a procedure...

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

Babai, a more accurate estimate vector can be obtained and the coefficients of the multiple polynomial of the interpolation polynomial can be computed.

computational complexity：计算复杂性

fundamental theorem of algebra：代数基本定理

horner：多项式计算

hermit Hermit 型 | horner 多项式计算 | invr 有理矩阵逆

parallel algorithm：并行算法

41、 并行算法(Parallel Algorithm) 是一些可同时执行的多个进程的集合,这些进程相互作用和协调工作,从而达到对给定问题的求解. 42、 数值计算(Numerical Computing) 是指基于代数关系运算的一类诸如矩阵计算、多项式求值、求解线性方程组等数字计算问题.

polynomial approximation method：多项式逼近法

polynomial approximation 多项式近似,多项式近似法 | polynomial approximation method 多项式逼近法 | polynomial arithmetic 多项式计算

Polynomial：计算多项式的值

MinMaxRunningResettable 输出信号的最小或最大值,带复位功能 | Polynomial 计算多项式的值 | Product 产生模块各输入的简积或商

polynomial reducible：多项式可归约[的]

Spline interpolation：样条插补

line 样条插补(Spline interpolation) 样条插补( ) 计算分段多项式 三次样条插补 10.3 conv deconv poly polyder polyfit polyint polyval polyvalm residue roots 多项式( 多项式(Polynomials) ) 多项式相乘 多项式相除 由根创建多项式 多项式微分 多项式拟合 积分多项式分析 求多项式的值 求矩阵多项式的值 求部分分式表达

transitive closure：传递闭包

MinMax Running Resettable：输出信号的最小或最大值,带复位功能

MinMax 输出信号的最小或最大值 | MinMax Running Resettable 输出信号的最小或最大值,带复位功能 | Polynomial 计算多项式的值