Sentence examples for be an arbitrary initial from inspiring English sources

Let be an arbitrary initial vector.

Let (x^{(0)}in mathbb{C}^{n}) be an arbitrary initial point.

Let (x^{(0)}inmathbb{C}^{n}) be an arbitrary initial point.

Let (x_{0}in) (Re_^{n}) be an arbitrary initial point.

Let (varepsilon _{1}in 0,A]) be an arbitrary number and (t_{0}in mathbb{R}_) be an arbitrary initial time.

Then f has a unique fixed point x ∗ ∈ ⋂ i = 1 r A i and the iterative sequence { x n } n ≥ 0 ( x n = f ( x n − 1 ), n ∈ N ) converges to x ∗ for any initial point x 0 ∈ Y. Proof Let x 0 ∈ Y be an arbitrary initial point.

(4.4) where (x_{0}in C) is an arbitrary initial guess.

Let the sequence { x n } be generated iteratively by (3.5): where x 0 ∈ C is an arbitrary initial guess.

where Z 0 ∈ X is an arbitrary initial guess of z 0 which is taken to be zero.

for all n ≥ 1, where x 1 is an arbitrary initial value, and { β n } is a sequence in [ 0, 1 ].

for all n ≥ 1, where x 1 is an arbitrary initial value, f is a real function, and { α n } is a sequence in [ 0, 1 ].