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References in periodicals archive ?
Algorithm 1: Conjugate gradient algorithm. (1) function CG (A, b, [x.sub.0], n) Input: A [member of] [R.sup.nxn], b [member of] [R.sup.n] [x.sub.0] [member of] [R.sup.n] Output: [x.sub.0] [member of] [R.sup.n] (2) [p.sub.0] = [r.sub.0] = b - A[x.sub.0] (3) i = 0 (4) repeat (5) [[alpha].sub.i] = [r.sup.T.sub.i][r.sub.i] / ([p.sub.i]).sup.T] (A[p.sub.i]) (6) [x.sub.i+1] = [x.sub.i] + ([[alpha].sub.i] x [p.sub.i]) (7) [r.sub.i+1] = [r.sub.i] - ([[alpha].sub.i] x A[p.sub.i]) (8) [[beta].sub.i] = [r.sup.T.sub.i+1][r.sub.i+1] / [r.sup.T.sub.i][r.sub.i] (9) [p.sub.i+1] = [r.sub.i+1] + [[beta].sub.i][p.sub.i] (10) i = i + 1 (11) until ([r.sub.i] is sufficiently small) (12) x = [x.sub.0] Algorithm 2: Interval modified conjugate gradient algorithm.
% Average Differences Result Metrics LM 5neurons LM 10neuron BR 5neurons BR 10neurons V 1,66 0,50 0,39 0,09 E 25,19 4,16 3,45 1,08 H 5,03 1,33 1,09 0,36 Result Metrics SCG 5neurons SCG 10neurons V 3,51 6,41 E 42,61 253,18 H 10,36 254,53 LM: Levenberg-Marquardt algorithm BR: Bayesian Regularization algorithm SCG: Scaled Conjugate Gradient algorithm Table 2.
Based on Table 1's sixteen kinds of scheme (different parameters set), we compared algorithm A with DY (given by formula (10)) conjugate gradient algorithm based on different initial point for three test problems.
A nonlinear conjugate gradient algorithm with an optimal property and an improved Wolfe line search.
In order to attempt to minimize the error E as a function of w using the scaled conjugate gradient algorithm as described above, the capability must exist for the efficient computation of the gradient E'(w) of E at w and multiplication of a vector by the Hessian matrix E"(w) of E at w.
Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization.
At PNNL, a parallel version of the conjugate gradient algorithm was developed in a shared-memory form.
A feedforward neural network with sigmoidal activation functions was used with a conjugate gradient algorithm to recognize the complex input-output relation between the paint properties and the formula components.
Below is most of the Solve method found in the HCL_PCG class, which implements the preconditioned conjugate gradient algorithm. It is worth emphasizing the truly generic nature of this code.
At present the hyperparameters of GPR are got by maximizing likelihood function of training samples based on conjugate gradient algorithm. However, this traditional algorithm embodies the disadvantages of too strong dependence of optimization effect on initial value, difficult determination of iteration steps, and easy falling into local optimum.
Therefore, the preconditioned global conjugate gradient algorithm is obtained by applying the preconditioner (4.10) to the normal equations associated with the matrix linear operator defined by (4.11).
Andrei, "A Dai-Yuan conjugate gradient algorithm with sufficient descent and conjugacy conditions for unconstrained optimization," Applied Mathematics Letters, vol.