Rank deficiencies and bifurcation into affine subspaces for separable parameterized equations
Yun-Qiu Shen, Tjalling J. Ypma · Mathematics of Computation · 2015
Many applications lead to separable parameterized equations of the form F ( y , μ , z ) ≡ A ( y , μ ) z + b ( y , μ ) = 0 F(y,\mu ,z) \equiv A(y, \mu )z+b(y, \mu )=0 , where y ∈ R n y \in \mathbb R^n , z ∈ R N z \in \mathbb R^N , A ( y , μ ) ∈ R ( N + n ) × N A(y, \mu ) \in \mathbb {R}^{(N+n) \times N} , b ( y , μ ) ∈ R N + n b(y, \mu ) \in \mathbb {R}^{N+n} and μ ∈ R \mu \in \mathbb R is a parameter. Typically N >> n N >>n