an:06393218
Zbl 1316.65049
Lauterbach, Reiner; Opfer, Gerhard
The Jacobi matrix for functions in noncommutative algebras
EN
Adv. Appl. Clifford Algebr. 24, No. 4, 1059-1073 (2014); erratum ibid. 24, No. 4, 1075 (2014).
00338916
2014
j
65F30 65F60
Jacobi matrices in algebras over \({\mathbb{R}^N}\); Jacobi matrices for polynomials over noncommutative algebras; Jacobi's matrix for the algebraic Riccati equation; Jacobi matrices for functions defined via Taylor and Laurent expansions over noncommutative algebras
The authors develop a general tool for constructing the exact Jacobi matrix for functions defined in noncommutative algebraic systems without using any partial derivative. The construction is applied to solving nonlinear problems of the form \(f(x) = 0\) with the aid of Newton's method in algebras defined in \({\mathbb{R}^N}\).
Zhihua Zhang (Beijing)