### Table 1: Speedups of automatically restructured linear algebra routines on Con#0Cg-

1991

"... In PAGE 12: ... The initial results were encouraging. Table1 shows the speedup results for a set of linear algebra routines. The #0Crst routine is a conjugate gradient algorithm #5B23#5D; the other routines are from Numerical Recipes #5B27#5D.... ..."

Cited by 22

### Table 1. MTL linear algebra operations.

1998

"... In PAGE 4: ...The MTL Generic Algorithms for Linear Algebra The Matrix Template Library provides a rich set of basic linear algebra opera- tions, roughly equivalent to the Level-1, Level-2 and Level-3 BLAS. Table1 lists the principle algorithms included in MTL. In the table, alpha and s are scalars, x,y,z are 1-D containers, A,B,C,E are row or column oriented matrices, U, L are upper and lower triangular matrices, and i is an iterator.... In PAGE 4: ... With BLAIS, the blocking sizes can be modi#0Ced at compile time through a few global constants, so that the algorithms can be customized for the memory hierarchy of a particular architecture. Note that in Table1 di#0Berent operations are not de#0Cned for each permutation of transpose, scaling, and striding. Instead, only one algorithm is provided, but it can be combined with the use of strided and scaled vector adapters, or the trans#28#29 method to create the permutations.... ..."

Cited by 7

### Table 1. MTL linear algebra operations.

1998

"... In PAGE 4: ...The MTL Generic Algorithms for Linear Algebra The Matrix Template Library provides a rich set of basic linear algebra opera- tions, roughly equivalent to the Level-1, Level-2 and Level-3 BLAS. Table1 lists the principle algorithms included in MTL. In the table, alpha and s are scalars, x,y,z are 1-D containers, A,B,C,E are row or column oriented matrices, U, L are upper and lower triangular matrices, and i is an iterator.... In PAGE 4: ... With BLAIS, the blocking sizes can be modi ed at compile time through a few global constants, so that the algorithms can be customized for the memory hierarchy of a particular architecture. Note that in Table1 di erent operations are not de ned for each permutation of transpose, scaling, and striding. Instead, only one algorithm is provided, but it can be combined with the use of strided and scaled vector adapters, or the trans() method to create the permutations.... ..."

Cited by 7

### TABLE 1 Leading complex floating-point operations for some basic linear algebra operations

1993

Cited by 4

### Table 2: Basic Linear Algebra Subroutines (BLAS) Operation De nition Floating Memory q

"... In PAGE 6: ... For a more complete list of the BLAS, see sec- tion 12. Table2 counts the number of memory references and oating points operations performed by three related BLAS. The last column gives the ratio q of ops to memory references.... In PAGE 6: ... The signi cance of q is that it tells us roughly how many ops we can perform per memory reference, or how much useful work we can do compared to the time moving data; therefore, the algorithms with the larger q values are better building blocks for other algorithms. Table2 re ects a hierarchy of operations: Operations like saxpy operate on vectors and o er the worst q values; these are called Level 1 BLAS [10], and include inner products and other simple operations. Operations like matrix{vector multiplication operate on matrices and vectors, and o er slightly better q values; these are called Level 2 BLAS [11], and include solving triangular systems of equations and rank-1 updates of matrices (A + xyT, x and y column vectors).... ..."

### Table 1: The linear algebra subroutines from BLAS and LAPACK used in the test programs.

1998

"... In PAGE 12: ... LAPACK uses the BLAS routines. The main work in this implementation is done in the factorisation, solving and multiplication routines; see Table1 for the speci c routines used. 5.... In PAGE 27: ...5 110.5 Table1 0: Some facts for the convergence tests 6.8.... ..."

Cited by 1

### Table 2: Basic Routing Algebras.

"... In PAGE 4: ... 2.3 Base Algebras Table2 presents a collection of simple routing algebras, together with their monotonicity property. Each algebra is now explained in turn.... ..."

### Table 2: Basic Algebraic Laws

"... In PAGE 28: ...18 4 The High Level Petri Box Calculus 4.1 Algebraic Laws Table2 contains a selection of Algebraic Equivalences which we conjecture hold for High Level Petri Boxes. The demonstration of these laws is left to another paper, here follows a brief description.... ..."