Finding the skew-symmetric solvent to a quadratic matrix equation
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Inthispaperweconsiderthequadraticmatrixequationwhich can be defined by Q(X) = AX^2 + BX + C = 0,where X is a n×n unknown real matrix; A,B and C are n×n given matrices with real elements. Newton’s method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr ́echet derivative is singular. Finally, we give some numerical examples.
Abstract
Inthispaperweconsiderthequadraticmatrixequationwhich can be defined by Q(X) = AX^2 + BX + C = 0,where X is a n×n unknown real matrix; A,B and C are n×n given matrices with real elements. Newton’s method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr ́echet derivative is singular. Finally, we give some numerical examples.
참고문헌 (11)
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