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The Linear Algebra Mapping Problem. Current State of Linear Algebra Languages and Libraries

https://doi.org/10.1145/3549935
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-49372-7_24openalex-snapshot
Arrays in Blitz++
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libflame
inferredcites →https://doi.org/10.1007/978-3-319-17248-4_10openalex-snapshot
On the Performance Prediction of BLAS-based Tensor Contractions
inferredcites →https://doi.org/10.1007/978-3-540-68942-3_4openalex-snapshot
Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation
inferredcites →https://doi.org/10.1007/978-3-540-72521-3_21openalex-snapshot
Register Allocation: What Does the NP-Completeness Proof of Chaitin et al. Really Prove? Or Revisiting Register Allocation: Why and How
inferredcites →https://doi.org/10.1007/978-3-642-23568-9_12openalex-snapshot
Knowledge-Based Automatic Generation of Partitioned Matrix Expressions
inferredcites →https://doi.org/10.1007/978-3-642-38718-0_33openalex-snapshot
A Domain-Specific Compiler for Linear Algebra Operations
inferredcites →https://doi.org/10.1016/0096-0551(81)90048-5openalex-snapshot
Register allocation via coloring
inferredcites →https://doi.org/10.1016/j.amc.2015.11.078openalex-snapshot
Large-scale linear regression: Development of high-performance routines
inferredcites →https://doi.org/10.1016/j.jocs.2017.04.005openalex-snapshot
A parallel implementation of the ensemble Kalman filter based on modified Cholesky decomposition
inferredcites →https://doi.org/10.1016/j.sigpro.2015.09.017openalex-snapshot
Sparsity-based correction of exponential artifacts
inferredcites →https://doi.org/10.1016/s0010-4655(98)00114-3openalex-snapshot
Maple programs for generating efficient FORTRAN code for serial and vectorised machines
inferredcites →https://doi.org/10.1038/s41586-020-2649-2openalex-snapshot
Array programming with NumPy
inferredcites →https://doi.org/10.1057/jors.1991.155openalex-snapshot
Introduction to Algorithms
inferredcites →https://doi.org/10.1080/10618600.1995.10474671openalex-snapshot
Differentiation of the Cholesky Algorithm
inferredcites →https://doi.org/10.1109/iccsa.2011.41openalex-snapshot
Automatic Generation of Loop-Invariants for Matrix Operations
inferredcites →https://doi.org/10.1109/icme.2000.869637openalex-snapshot
Automatic audio segmentation using a measure of audio novelty
inferredcites →https://doi.org/10.1109/icnc.2011.62openalex-snapshot
Accelerating the Dynamic Programming for the Matrix Chain Product on the GPU
inferredcites →https://doi.org/10.1109/icpads.2012.97openalex-snapshot
Model-driven Level 3 BLAS Performance Optimization on Loongson 3A Processor
inferredcites →https://doi.org/10.1109/ipdps.2008.4536183openalex-snapshot
Build to order linear algebra kernels
inferredcites →https://doi.org/10.1109/sc.2016.83openalex-snapshot
LIBXSMM: Accelerating Small Matrix Multiplications by Runtime Code Generation
inferredcites →https://doi.org/10.1109/superc.1990.129995openalex-snapshot
LAPACK: A portable linear algebra library for high-performance computers
inferredcites →https://doi.org/10.1109/tc.1973.5009181openalex-snapshot
Comments on "The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement
inferredcites →https://doi.org/10.1109/tc.1973.5009182openalex-snapshot
On Efficient Computation of Matrix Chain Products
inferredcites →https://doi.org/10.1109/tip.2018.2875569openalex-snapshot
Image Restoration by Iterative Denoising and Backward Projections
inferredcites →https://doi.org/10.1109/tpds.2003.1195411openalex-snapshot
Processor allocation and task scheduling of matrix chain products on parallel systems
inferredcites →https://doi.org/10.1109/tpds.2015.2401575openalex-snapshot
Evaluation Criteria for Sparse Matrix Storage Formats
inferredcites →https://doi.org/10.1109/tsp.2011.2166546openalex-snapshot
Concentration of Measure for Block Diagonal Matrices With Applications to Compressive Signal Processing
inferredcites →https://doi.org/10.1115/1.3662552openalex-snapshot
A New Approach to Linear Filtering and Prediction Problems
inferredcites →https://doi.org/10.1137/0211028openalex-snapshot
Computation of Matrix Chain Products. Part I
inferredcites →https://doi.org/10.1137/1.9780898718027openalex-snapshot
Accuracy and Stability of Numerical Algorithms
inferredcites →https://doi.org/10.1137/110830125openalex-snapshot
Expression Templates Revisited: A Performance Analysis of Current Methodologies
inferredcites →https://doi.org/10.1137/141000671openalex-snapshot
Julia: A Fresh Approach to Numerical Computing
inferredcites →https://doi.org/10.1137/16m1062053openalex-snapshot
Randomized Quasi-Newton Updates Are Linearly Convergent Matrix Inversion Algorithms
inferredcites →https://doi.org/10.1137/s0895479897326432openalex-snapshot
Tikhonov Regularization and Total Least Squares
inferredcites →https://doi.org/10.1145/1055531.1055533openalex-snapshot
Representing linear algebra algorithms in code: the FLAME application program interfaces
inferredcites →https://doi.org/10.1145/1274971.1274989openalex-snapshot
Representation-transparent matrix algorithms with scalable performance
inferredcites →https://doi.org/10.1145/1356052.1356053openalex-snapshot
Anatomy of high-performance matrix multiplication
inferredcites →https://doi.org/10.1145/1377603.1377606openalex-snapshot
Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
inferredcites →https://doi.org/10.1145/1498765.1498785openalex-snapshot
Roofline
inferredcites →https://doi.org/10.1145/2560421openalex-snapshot
Computing Petaflops over Terabytes of Data
inferredcites →https://doi.org/10.1145/2588555.2610519openalex-snapshot
LINVIEW
inferredcites →https://doi.org/10.1145/2764454openalex-snapshot
BLIS: A Framework for Rapidly Instantiating BLAS Functionality
inferredcites →https://doi.org/10.1145/2832080.2832084openalex-snapshot
A parallel ensemble Kalman filter implementation based on modified Cholesky decomposition
inferredcites →https://doi.org/10.1145/2840728.2840762openalex-snapshot
On a Natural Dynamics for Linear Programming
inferredcites →https://doi.org/10.1145/2854038.2854060openalex-snapshot
A basic linear algebra compiler for structured matrices
inferredcites →https://doi.org/10.1145/2909437.2909442openalex-snapshot
clSPARSE
inferredcites →https://doi.org/10.1145/3061664openalex-snapshot
Algorithm 979
inferredcites →https://doi.org/10.1145/3168804openalex-snapshot
The generalized matrix chain algorithm
inferredcites →https://doi.org/10.1145/3168812openalex-snapshot
Program generation for small-scale linear algebra applications
inferredcites →https://doi.org/10.1145/3204919.3204924openalex-snapshot
CLBlast
inferredcites →https://doi.org/10.1145/3210754openalex-snapshot
BLASFEO
inferredcites →https://doi.org/10.1145/3394277.3401836openalex-snapshot
Automatic Generation of Efficient Linear Algebra Programs
inferredcites →https://doi.org/10.1145/3446632openalex-snapshot
Linnea
inferredcites →https://doi.org/10.1145/355841.355847openalex-snapshot
Basic Linear Algebra Subprograms for Fortran Usage
inferredcites →https://doi.org/10.1145/365723.365732openalex-snapshot
PSBLAS
inferredcites →https://doi.org/10.1145/42288.42291openalex-snapshot
An extended set of FORTRAN basic linear algebra subprograms
inferredcites →https://doi.org/10.1145/504210.504213openalex-snapshot
FLAME
inferredcites →https://doi.org/10.1145/77626.79170openalex-snapshot
A set of level 3 basic linear algebra subprograms
inferredcites →https://doi.org/10.11588/heidok.00010856openalex-snapshot
A Parallel Algebraic Multigrid Method for Elliptic Problems with Highly Discontinuous Coefficients
inferredcites →https://doi.org/10.1177/1094342013492178openalex-snapshot
A case study in mechanically deriving dense linear algebra code
inferredcites →https://doi.org/10.21105/joss.00026openalex-snapshot
Armadillo: a template-based C++ library for linear algebra
inferredcites →https://doi.org/10.32614/r.manualsopenalex-snapshot
R: A Language and Environment for Statistical Computing
inferredcites →https://doi.org/10.48550/arxiv.1806.01437openalex-snapshot
PETSc/TS: A Modern Scalable ODE/DAE Solver Library
inferredcites →https://doi.org/10.5555/509058.509096openalex-snapshot
Automatically Tuned Linear Algebra Software
inferredcites →https://doi.org/10.5860/choice.34-0981openalex-snapshot
Accuracy and stability of numerical algorithms

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Tiling-Aware Vectorization Framework for Perfect Loop Nests in MLIR
inferred← citeshttps://doi.org/10.1007/978-981-95-9846-5_14openalex-snapshot
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Tensor Program Superoptimization through Cost-Guided Symbolic Program Synthesis
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Compilation of Generalized Matrix Chains with Symbolic Sizes
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Armadillo: an Efficient Framework for Numerical Linear Algebra
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inferred← citeshttps://doi.org/10.1145/3589246openalex-snapshot
Proceedings of the 9th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming
inferred← citeshttps://doi.org/10.1145/3589246.3595373openalex-snapshot
Towards Structured Algebraic Programming
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Teaching cases of eigenvalues and eigenvectors in the context of artificial intelligence
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Finch: Sparse and Structured Tensor Programming with Control Flow
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PyArmadillo: a streamlined linear algebra library for Python
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High-Performance Hybrid Algorithm for Minimum Sum-of-Squares Clustering of Infinitely Tall Data
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