Autoencoders are neural networks that are characterized by having the same inputs and outputs. This kind of Neural Networks aim to estimate a nonlinear transformation whose parameters allow to represent the input patterns to the network. The Extreme Learning Machine (ELM-AE) Autoencoders have random weights and biases in the hidden layer, and compute the output parameters by solving an overdetermined linear system using the Moore-Penrose Pseudoinverse. ELM-AE training is based on the Fast Iterative Shrinkage-Thresholding (FISTA). In this paper, we propose to improve the convergence speed obtained by FISTA considering the use of two algorithms of the Shrinkage-Thresholding class, namely Greedy FISTA and Linearly-Convergent FISTA. 6 frequently used public machine learning datasets were considered: MNIST, NORB, CIFAR10, UMist, Caltech256, Stanford Cars. Experiments were carried out varying the number of neurons in the hidden layer of the Autoencoders, considering the 3 algorithms, for all the databases. The experimental results showed that Greedy FISTA and Linearly-Convergent FISTA presented higher convergence speed, increasing the speed of ELM-Autoencoder training, maintaining a comparable generalization error between the three Shrinkage-Thresholding algorithms.