Nonlinear Equations - UFRJ

174 BIBLIOGRAPHY
α 0 – The constant 13−3√ 17
4
. 97
r 0 (α) – The function 1+α−√ 1−6α+α 2
4α
. 97
r 1 (α) – The function 1−3α−√ 1−6α+α 2
4α
. 97
σ 1 , . . . , σ n – Singular values associated to a matrix. 107
µ(f, x) – Ordinary condition number. 116
µ(f, x) – Invariant condition number. 117
N(F, X) – Pseudo-Newton iteration 123
A † – Pseudo-inverse o matrix A. 123
β(F, X) – Invariant related to pseudo-Newton iteration 125
γ(F, X) – Invariant related to pseudo-Newton iteration 125
α(F, X) – Invariant related to pseudo-Newton iteration 125
d proj (X, Y) – Projective distance. 127
dH d – Zero average, unit variance normal probab. distrib. 135
V – Solution variety 138
Σ ′ – Discriminant variety in V. 138
L(f t ; a, b) – Condition length 138
µ F (, ) – Frobenius condition number 139
Φ t,σ – Invariant associated to homotopy. 139