An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
LAPACK's user's guide
SIAM Journal on Matrix Analysis and Applications
Solution of the Sylvester matrix equation AXBT + CXDT = E
ACM Transactions on Mathematical Software (TOMS)
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Family of High-Performance Matrix Multiplication Algorithms
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
Representing linear algebra algorithms in code: the FLAME application program interfaces
ACM Transactions on Mathematical Software (TOMS)
Parallel out-of-core computation and updating of the QR factorization
ACM Transactions on Mathematical Software (TOMS)
Extracting SMP parallelism for dense linear algebra algorithms from high-level specifications
Proceedings of the tenth ACM SIGPLAN symposium on Principles and practice of parallel programming
Block variants of Hammarling's method for solving Lyapunov equations
ACM Transactions on Mathematical Software (TOMS)
Scalable parallelization of FLAME code via the workqueuing model
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Solving dense linear systems on platforms with multiple hardware accelerators
Proceedings of the 14th ACM SIGPLAN symposium on Principles and practice of parallel programming
ACM Transactions on Mathematical Software (TOMS)
Knowledge-based automatic generation of partitioned matrix expressions
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Rapid development of high-performance linear algebra libraries
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Automatic derivation of linear algebra algorithms with application to control theory
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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In this paper we apply a formal approach for the derivation of dense linear algebra algorithms to the triangular Sylvester equation. The result is a large family of provably correct algorithms. By using a coding style that reflects the algorithms as they are naturally presented, the correctness of the algorithms carries through to the correctness of the implementations. Analytically motivated heuristics are used to subsequently choose members from the family that can be expected to yield high performance. Finally, we report performance on the Intel (R) Pentium (R) III processor that is competitive with that of recursive algorithms reported previously in the literature for this operation.