Algebraic Algorithms
Algebraic Algorithms
复制标题
代数算法
DOI：
10.1201/9781420049503-c17
复制
发表时间：
1999
影响因子：
2.4
通讯作者：
Elias P. Tsigaridas
中科院分区：
文献类型：
--
作者：
Ioannis Z. Emiris;V. Pan;Elias P. Tsigaridas
这是关于即将到来的计算机手册中的代数算法的章节的初步版本，CRC Press/Taylor和Francis Group涉及代数算法。差分多项式，有理函数，代数集，曲线和表面。科学，工程以及信号和图像处理中的现代计算的基础。分解（反过Cholesky因素化以及特征值和单数值分解），计算矩阵特征和最小多项式的计算，确定词，Smith和Frobenius正常形式，等级以及（广义）倒置，单变量和多变量多元型结果，牛顿的多元级别，牛顿的多元级别，以及牛顿的多层次，以及牛顿的多元性师具有截短序列和代数集的常见倍数和操纵。无限精度的计算计算机图书馆和计算机代数
This is a preliminary version of a Chapter on Algebraic Algorithms in the upcoming Computing Handbook Set Computer Science (Volume I), CRC Press/Taylor and Francis Group. Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is most fundamental for modern computations in Sciences, Engineering, and Signal and Image Processing. They include the solution of a polynomial equation and linear and polynomial systems of equations, univariate and multivariate polynomial evaluation, interpolation, factorization and decompositions, rational interpolation, computing matrix factorization and decompositions (which in turn include various triangular and orthogonal factorizations such as LU, PLU, QR, QRP, QLP, CS, LR, Cholesky factorizations and eigenvalue and singular value decompositions), computation of the matrix characteristic and minimal polynomials, determinants, Smith and Frobenius normal forms, ranks, and (generalized) inverses, univariate and multivariate polynomial resultants, Newton’s polytopes, greatest common divisors, and least common multiples as well as manipulation with truncated series and algebraic sets. Such problems can be solved based on the error-free symbolic computations with infinite precision. The computer library GMP and computer algebra