Matrix Transformation for Optimization Calculation Accuracy
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Solution Overview
Problem
Existing calculating devices face challenges in achieving high calculation accuracy for optimization problems, particularly in matrix transformation and variable update processes.
Innovation Solution
A calculating device is configured with a processor that performs matrix transformation processing by deriving a second matrix through normalization of first row vectors and updates variable sets using specific multiply-add operations, allowing for repeated update processing with adjustable parameters to enhance accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional matrix transformation and variable update methods are used, then the calculation process is simple, but the calculation accuracy for optimization problems is insufficient
Solution Approach 1:
The patent transforms the input matrix through parameter changes (normalization of row vectors) before performing variable updates. This transformation modifies the parameter representation of the problem data to improve calculation accuracy while maintaining a structured processing approach
Solution Approach 2:
The calculation process is segmented into distinct stages: matrix transformation phase (normalizing row vectors) and variable update phase (updating variable sets using transformed matrix). This segmentation allows each phase to be optimized independently for accuracy
2Measurement precision
If iterative update processing is performed multiple times, then calculation precision improves, but calculation time increases
Solution Approach 1:
The matrix transformation (normalization of row vectors) is performed as a preliminary action before the iterative variable updates. This preprocessing step improves the convergence properties of subsequent iterations, allowing fewer iterations to achieve the desired precision
Solution Approach 2:
The iterative update process uses feedback from previous iteration results to adjust variable sets. The transformed matrix provides improved feedback signals that guide the optimization more efficiently toward the solution, reducing the number of iterations needed
Data Source
AI summary
According to one embodiment, a calculating device includes a processor configured to perform a matrix transformation processing, and an update processing. The matrix transformation processing includes deriving a second matrix by transforming first row vectors included in a first matrix. The update processing includes an update of first and second variable sets. The update of the second variable set includes obtaining the second variable set after the update by adding a first update function of the updated first variable set to the second variable set. The first update function includes at least one of first or second multiply-add operation. The first multiply-add operation includes a multiply-add operation of the updated first variable set and a component of the second matrix. The second multiply-add operation includes a multiply-add operation of a component of the second matrix and a variable dependent on the updated first variable set.