Using CORDIC to perform the QR Factorization System

THE COMPILATION OF COMPLEX MATRICES Using Coordinate Rotation Digital Computer to perform the QR Factorization System

• A good way to write an algorithm intended for a fixed-point target is to write it in MATLAB using built-in floating-point types so we can verify that the algorithm works. When we refine the algorithm to work with fixed-point types, then the best thing to do is to write it so that the same code continues working with floating-point. That way, when we are debugging, then we can switch the inputs back and forth between floating-point and fixed-point types to determine if a difference in behavior is because of fixed-point effects such as overflow and quantization versus an algorithmic difference. Even if the algorithm is not well suited for a floating-point target (as is the case of using CORDIC in the following case), it is still advantageous to have your MATLAB code work with floating-point for debugging purposes. In contrast, we may have a completely different strategy if our target is floating point. For example, the QR algorithm is often done in floating-point with Householder transformations and row or column pivoting. But in fixed-point it is often more efficient to use CORDIC to apply Givens rotations with no pivoting.