Iterative algorithm for vector rotations using minimal real number multiplications

This paper presents an efficient iterative algorithm for performing counterclockwise rotations on a 2-element real number vector, minimizing the number of real number multiplications required. By leveraging intermediate results from previous rotations, the algorithm achieves each subsequent rotation with only two real number multiplications. We analyze the mathematical foundation of the rotation process, detail the iterative update mechanism, and evaluate the computational efficiency of the approach. The algorithm’s simplicity and reduced computational cost make it suitable for applications requiring repeated vector rotations, such as computer graphics, signal processing, and robotics. We also discuss potential extensions and limitations of the method.