We propose a robust and fast solution for the inverse kinematic problem of general serial manipulators - i.e. any number and any combination of revolute and prismatic joints. The algorithm only requires the Denavit-Hartenberg (D-H) representation of the robot as input and no training or robot-dependent optimization function is needed. In order to handle singularities and to overcome the possibility of multiple paths in redundant robots, our approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire configuration of the end-effector. But unlike other iterative methods, our method achieves sub-millimeter accuracy in 20.48ms in average. The algorithm was implemented in C/C++ using 16 POSIX threads, and it can be easily expanded to use more threads and/or many-core GPUs. We demonstrate the high accuracy and the real-time performance of our method by testing it with five different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot.