Abstarct: Gravity and magnetic methods which are called potential field methods in geophysics, are important geophysical methods in mineral exploration. Inversion of potential field data is the most important method in interpretation of the data. Most of inversion methods in geophysics need large amount of computer memory and calculation time. Reducing required time and memory in inversion of geophysical data especially potential field data is an important topic for research. The aim of this study is to provide new algorithms for smooth inversion, focusing inversion and inversion in data space with sparseness constrain to improve speed of inversion. In order to achieve the above objectives, forward solution and Lanczos Bidiagonalization codes prepared in MATLAB for smooth inversion. Then, the preconditioned Lanczos Bidiagonalization (LB) method with discrete cosine transform basis vector were presented to increase speed and decrease the required memory of LB algorithm. It was also showed that Normalized Cumulative Periodogram (NCP) method is a suitable and fast method for choosing regularization parameter. In addition the LB method is used to improve speed of the focusing inversion and inversion in data space with sparseness constrain of potential field data and finally the improved inversion algorithms were developed. The improved algorithms were tested on data obtained from 2D and 3D synthetic models and some sets of field data. The results were then compared with other exploration data and the performance of the improved algorithms were confirmed. The results showed that in smooth inversion the required memory is decreased to one sixth and the required inversion time is decreased 60 percent with using preconditioned Lanczos Bidiagonalization. The improved algorithms of focusing inversion and inversion in data space with sparseness constrain are also at least 20 percent and 10 percent faster than common algorithms.