A preconditioned conjugate gradient (PCG) solver, embedded in an electronic device to perform a simultaneous localization and mapping (SLAM) operation, includes an image database, a factor graph database, and a back-end processor, wherein the back-end processor is configured to receive an image from the image database to perform re-localization, receive, from the factor graph database, data for calculating six degrees of freedom (DoF)-related components, construct a matrix including the six degrees of freedom-related components based on the received data, and load and rearrange the matrix and a vector, to perform calculation on each block of each row of the matrix and the vector, then output first data, and shift second data to a location of the first data.