Condition Numbers and Backward Error of a Matrix Polynomial Equation Arising in Stochastic Models
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DOI: 10.1007/s10915-018-0641-x
Abstract: We consider a matrix polynomial equation (MPE) $$A_nX^n+A_{n-1}X^{n-1}+\cdots +A_0=0$$AnXn+An-1Xn-1+⋯+A0=0, where $$A_n, A_{n-1},\ldots , A_0 \in \mathbb {R}^{m\times m}$$An,An-1,…,A0∈Rm×m are the coefficient matrices, and $$X\in \mathbb {R}^{m\times m}$$X∈Rm×m is the unknown matrix. A sufficient condition for… read more here.
Keywords: polynomial equation; matrix polynomial; condition numbers; backward error ... See more keywords
Accurate two-frame random phase retrieval: an integrated approach using quartic polynomial equation solving augmented by least squares method
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DOI: 10.1117/1.oe.64.3.034101
Abstract: Abstract. To extract the phase distribution with higher accuracy in phase-shifting interferometry, a random two-step hybrid phase retrieval approach by combining the quartic polynomial equation solving method and the least squares iterative algorithm (Hybrid QPE+LSI)… read more here.
Keywords: polynomial equation; least squares; quartic polynomial; phase retrieval ... See more keywords