Asif Vaismann

Two Inequivalent Ternary Rank-176 Decompositions of ⟨5,7,7⟩ over ℤ with Fewer Atom Types than the Published Solution

We report two inequivalent exact algorithms for the product of a 5×7 by a 7×7 matrix, each using 176 multiplications in which every coefficient is −1, 0 or +1. Rank 176 is the best rank published for ⟨5,7,7⟩ in any coefficient domain; the rank-176 scheme in the public catalogue c...

Two Inequivalent Ternary Rank-176 Decompositions of ⟨5,7,7⟩ over ℤ with Fewer Atom Types than the Published Solution

We report two inequivalent exact algorithms for the product of a 5×7 by a 7×7 matrix, each using 176 multiplications in which every coefficient is −1, 0 or +1. Rank 176 is the best rank published for ⟨5,7,7⟩ in any coefficient domain; the rank-176 scheme in the public catalogue c...

Three Inequivalent Ternary Rank-144 Decompositions of ⟨4,7,7⟩ over ℤ

We report three mutually inequivalent exact algorithms for the product of a 4×7 by a 7×7 matrix, each using 144 multiplications in which every coefficient is −1, 0 or +1. Rank 144 is the best rank published for ⟨4,7,7⟩ in any coefficient domain; the rank-144 scheme in the public...

Four Inequivalent Ternary Rank-90 Decompositions of ⟨3,5,8⟩ over ℤ

We report four mutually inequivalent exact algorithms for the product of a 3×5 by a 5×8 matrix, each using 90 multiplications in which every coefficient is −1, 0 or +1. Rank 90 is the best rank published for ⟨3,5,8⟩ in any coefficient domain; the rank-90 scheme in the public cata...

Four Inequivalent Ternary Rank-90 Decompositions of ⟨3,5,8⟩ over ℤ

We report four mutually inequivalent exact algorithms for the product of a 3×5 by a 5×8 matrix, each using 90 multiplications in which every coefficient is −1, 0 or +1. Rank 90 is the best rank published for ⟨3,5,8⟩ in any coefficient domain; the rank-90 scheme in the public cata...

Two Inequivalent Ternary Rank-104 Decompositions of ⟨4,5,7⟩ over ℤ

We report two inequivalent exact algorithms for the product of a 4×5 by a 5×7 matrix, each using 104 multiplications in which every coefficient is −1, 0 or +1. Rank 104 is the best rank published for ⟨4,5,7⟩ in any coefficient domain; the rank-104 scheme in the public catalogue c...

Two Inequivalent Ternary Rank-104 Decompositions of ⟨4,5,7⟩ over ℤ

We report two inequivalent exact algorithms for the product of a 4×5 by a 5×7 matrix, each using 104 multiplications in which every coefficient is −1, 0 or +1. Rank 104 is the best rank published for ⟨4,5,7⟩ in any coefficient domain; the rank-104 scheme in the public catalogue c...

Three Inequivalent Ternary Rank-144 Decompositions of ⟨4,7,7⟩ over ℤ

We report three mutually inequivalent exact algorithms for the product of a 4×7 by a 7×7 matrix, each using 144 multiplications in which every coefficient is −1, 0 or +1. Rank 144 is the best rank published for ⟨4,7,7⟩ in any coefficient domain; the rank-144 scheme in the public...