Algebraic methods applied to the reconstruction of Sparse-view Computed Tomography (CT) can provide both a high image quality and a decrease in the dose received by patients, although with an increased reconstruction time since their computational costs are higher. In our work, we present a new algebraic implementation that obtains an exact solution to the system of linear equations that models the problem and based on single-precision floating-point arithmetic. By applying Out-Of-Core (OOC) techniques, the dimensions of the system can be increased regardless of the main memory size and as long as there is enough secondary storage (disk). These techniques have allowed to process images of 768 x 768 pixels. A comparative study of our method on a GPU using both single-precision and double-precision arithmetic has been carried out. The goal is to assess the single-precision arithmetic implementation both in terms of time improvement and quality of the reconstructed images to determine if it is sufficient to consider it a viable option. Results using single-precision arithmetic approximately halves the reconstruction time of the double-precision implementation, whereas the obtained images retain all internal structures despite having higher noise levels.