Mixed Precision Linear Equation Solver

The patent applies local quality by using different precision levels for different computational operations within the same system. Specifically, it identifies and separates the most computationally expensive operation (typically matrix-vector multiplication) to be performed in low precision, while other operations are performed in high precision. This localized application of precision optimization resolves the contradiction by allowing speed improvements in critical paths without compromising overall computation accuracy.

The patent segments the computational process into distinct precision domains. It divides the iterative algorithm into operations that can tolerate low precision (such as the dominant computational kernel) and operations that require high precision (such as convergence checking and parameter updates). This segmentation enables the system to achieve high productivity in the segmented low-precision portion while maintaining accuracy in the high-precision portions.

The patent applies local quality by assigning different precision characteristics to different parts of the computational workflow. The most energy-intensive operation (matrix-vector multiplication) is designated for low precision execution to maximize energy efficiency, while other operations maintain high precision to ensure solution accuracy. This localized precision strategy resolves the energy-accuracy contradiction.

The patent dynamically changes the precision parameter based on the specific operation being performed. Instead of using a fixed precision level for all operations, it adjusts the precision parameter locally for each computational step, setting low precision for the dominant operation and high precision for other operations. This parameter change strategy enables energy-efficient computation without sacrificing solution accuracy.

The patent applies local quality by selectively applying high precision only where necessary for maintaining solution accuracy, rather than uniformly across all operations. The dominant computational operation is executed in low precision since it benefits most from speed and energy efficiency, while high precision is applied only to operations critical for accuracy. This resolves the contradiction by localizing high precision usage.

The patent segments the computational process into high-precision and low-precision portions. By identifying that the most expensive operation can be performed in low precision without significantly impacting final accuracy, it segments this operation from the rest of the workflow that requires high precision. This segmentation reduces overall energy consumption while maintaining solution accuracy.

The patent applies local quality by using low precision for the most computationally expensive operation (matrix-vector multiplication) where speed benefits are most significant, while maintaining high precision for other operations. This localized precision optimization resolves the speed-accuracy contradiction by allowing fast computation in the critical path without compromising overall solution accuracy.

The patent segments the computational workflow into speed-critical operations (performed in low precision) and accuracy-critical operations (performed in high precision). By segmenting the dominant operation from the rest of the workflow and assigning it low precision, the system achieves significant speed improvements while maintaining acceptable solution accuracy through the high-precision segments.