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The Jacobi matrix for functions in noncommutative algebras. (English) Zbl 1316.65049
Adv. Appl. Clifford Algebr. 24, No. 4, 1059-1073 (2014); erratum ibid. 24, No. 4, 1075 (2014).
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 $${\mathbb{R}^N}$$.

##### MSC:
 65F30 Other matrix algorithms (MSC2010) 65F60 Numerical computation of matrix exponential and similar matrix functions
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##### References:
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