Complex Mathematical Operations TRIZ Cases
- Cell-Based Path Planning for Mobile Robots
A cell decomposition algorithm reduces generated cells by connecting obstacle vertices and dividing vertical angles.
- Two-Dimensional Data Transform Device Storage Access Reduction
A two-dimensional data transform device segments matrix processing into row and column phases to reduce auxiliary storage access frequency.
- Integrated Summation Matrix for Low Latency Tensor Computing
ISUM TCS generates integrated matrices to compute sum-products without separate addition steps.
- Resistive Processing Unit Preconditioner for Linear Equation Solvers
A resistive processing unit stores a preconditioning matrix to perform analog matrix-vector multiplication.
- Dynamic Covariance Estimation via Low-Rank Sparse Decomposition
Decomposes covariance matrices into low-rank and sparse parts to resolve estimation complexity while capturing time-varying dependencies.
- Network Flow Graph Intermediate Representation for Heuristic Optimization
A network flow graph intermediate representation models optimization problems to enable programmatic analysis of heuristic solutions.
- Non-Volatile Memory Array Solving Partial Differential Equations
Segmenting sparse coefficient matrices into sub-matrices within a non-volatile memory array reduces energy consumption from data transfer bottlenecks.
- Matrix Partitioning for Torus Computing Element Coordination
Least common multiple partitioning distributes submatrices across torus-connected elements, eliminating waiting times from overlapping usage.
- Correlation Management System for Asset Attribute Influence Ranking
A correlation management system ranks asset attributes by influence to configure preferred values.
- Delay-encoded harmonic ultrasound imaging for clutter noise reduction
Delay-encoded harmonic ultrasound imaging applies temporal delays to encode emissions and recover signals via frequency domain decoding.
- Configurable FFT Pipeline Architecture for Multi-Size Processing
A configurable pipelined FFT architecture uses multiplexers to select stage outputs based on required size.
- Seasonal Effect Identification in Time Series Data
Spectral analysis identifies seasonal cycle lengths to eliminate human bias and ensure consistent forecasting reliability.
- FFT Circuit Address Logic for FPGA Resource Reduction
Radix-based address calculation eliminates reordering modules, reducing FPGA circuit area and critical path delays.
- Time-series Data Accumulation with Interval Function Determination
Calculates intervals to store statistical value data, preserving old data influence without deleting information below significance thresholds.
- Transformer Attention Acceleration via Tensor Grouping
Aligns tensor dimensions with multiplication engine capabilities to reduce latency, power usage, and heat generation in large datasets.
- QR Factorization Matrix Update for Reduced Computation Time
A data processing system reuses intermediate QR factorization results to update matrices without full recomputation.
- Optimal Transport Data Preprocessing for Algorithmic Fairness
Optimal transport computes sample-level weights to preprocess classification datasets, reducing disparities while preserving original data integrity.
- Automatic Analyzer Abnormality Identification via Uncertainty Calculation
An automatic analyzer calculates combined uncertainty estimates from analysis parameters to identify device-side abnormalities during quality control.
- Mahalanobis-Taguchi Anomaly Detection with Importance Scores
Anomaly detection system uses Mahalanobis distance and importance scores to identify responsible attributes.
- Matrix Multiplication Engine Pipelining
Pipelined multiply-accumulate units execute operations in parallel, reducing time complexity from O(n^3) to O(n^2).
- Parallel Multicolor ILU Preconditioner for Sparse Linear Systems
Graph coloring identifies parallelisms in sparse linear systems to compute incomplete LU factors, reducing computational complexity and memory requirements.
- Matrix Processing Unit Parallel Dot Product Computation
Splitting matrices allows concurrent partial dot product calculation, reducing processing cycles and enhancing parallelism in data systems.
- Arctangent Computation via Lookup Table Segmentation
Segmenting the angle allows polynomial approximation and lookup correction to resolve speed versus accuracy trade-offs.
- Tensor Core Sparse Matrix Multiplication via Offline Compaction
Offline compaction reorganizes unstructured sparse matrices to eliminate load imbalance and reduce hardware overhead during tensor core multiplication.
- Iterative Fourier Transform for Light Waveform Control
A data creation apparatus calculates phase and intensity spectra using iterative Fourier transforms to shape light waveforms.
- Vector Decomposition and Quantization for Neural Network Data Processing
A data processing apparatus performs vector decomposition and quantization to handle diverse data distributions.
- Dynamic Interval Width Adjustment for Frequency Distribution Data
A frequency distribution data generation device dynamically adjusts interval width to optimize processing speed.
- Cross-Modal Search Embedding Bins and Extended Relevance Matrices
Segmenting the embedding space into bins improves retrieval ranking while extending relevance matrices captures caption similarities that boost search accuracy.
- Self-Contrastive Decorrelation for Sentence Embedding Training
A self-contrastive decorrelation technique trains machine learning models using augmented sentence views.
- Multilinear Discriminant Analysis Via Invariant Theory
Invariant theory optimization computes coordinate changes for multilinear data sets, preserving tensor rank and spatial locality lost during vectorization.
- Correlator With Selectable Processing Logic
A correlator circuit uses selectable processing logic to handle data and coefficient values through a programmable fabric.
- Shapley Value Computation via Functional Decomposition
Segments models into lower-order terms to compute exact Shapley values, reducing computational complexity while maintaining accuracy.
- Tensor Radial Basis Networks for High-Dimensional ODE Solving
Tensor radial basis networks embed ordinary differential equations into matrix product states.
- Microcontroller FFT Butterfly Operation Latency
A microcontroller performs Fast Fourier Transform butterfly operations before all signal samples arrive.
- Adaptive Lifting Wavelet Transform for Image Compression
An adaptive lifting method reduces rounding errors and improves compression ratios by adjusting prediction orders based on local image statistics.
- Jacobian Graph Linearization for Dynamic System Sensitivity Analysis
Graph theoretic optimizations reduce memory usage and computational intensity during sensitivity analysis of complex dynamic systems.
- Sparse Matrix Arithmetic Hardware Using Bitmap Scheduling
A scheduler generates instruction schedules from a bitmap to direct an arithmetic circuit on sparse matrix operations.
- Parallel Maximum Subset Sum Calculation via SIMD Segmentation
Segmented array blocks processed in parallel via SIMD instructions reduce computational complexity and enable real-time streaming data analysis.
- Matrix Decomposition Search Optimization via Gradient-Based Evaluation
A data processing program updates matrix elements to solve decomposition problems using continuous parameter changes.
- Pair-Wise Interaction Detection for Large Variable Sets
Segmenting variables into groups reduces computational intensity while maintaining detection accuracy for pair-wise interactions.
- Parameter Search Apparatus for Balancing Performance and Efficiency
A parameter search apparatus constructs an objective function model to select optimal manufacturing values.
- Fast Digital Curvelet Transform for Sparse Edge Representation
Fast digital curvelet transforms replace wavelets to resolve suboptimal sparsity in edge representation through O(n^2 log n) complexity.