alternative basis

DPS_CoBL.m

@@ -1,6 +1,6 @@
 function M = DPS_CoBL(A, nmin)
 %          Left change of basis of the sparsification
-%          of DPS's algorithm via alternate basis.
+%          of DPS's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

DPS_CoBR.m

@@ -1,6 +1,6 @@
 function M = DPS_CoBR(A, nmin)
 %          Right change of basis of the sparsification
-%          of DPS's algorithm via alternate basis.
+%          of DPS's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

DPS_ICoB.m

@@ -1,6 +1,6 @@
 function M = DPS_ICoB(A, nmin)
 %          Inverse change of basis of the sparsification
-%          of DPS's algorithm via alternate basis.
+%          of DPS's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

DPS_alternate.m

@@ -1,6 +1,6 @@
 function C = DPS_alternate(A, B, nmin)
 %          Sparsification of DPS's algorithm
-%          via alternate basis.
+%          via alternative basis.
 
 %          Reference:
 %          G. Beniamini, N. Cheng, O. Holtz, E. Karstadt, O. Schwartz;

DPS_mul.m

@@ -1,6 +1,6 @@
 function C = DPS_mul(A, B, nmin)
 %          Sparse multiplication of the sparsification
-%          of DPS's algorithm via alternate basis.
+%          of DPS's algorithm via alternative basis.
 
 if nargin < 3, nmin = 8; end
 

README.md

@@ -30,7 +30,7 @@ created for the numerical experiments of the paper:
 
 
 **Faster Algorithms**:
-Faster variants, using an alternate basis from:
+Faster variants, using an alternative basis from:
 - [G. Beniamini, N. Cheng, O. Holtz, E. Karstadt, O. Schwartz; Sparsifying the Operators of Fast Matrix Multiplication Algorithms](https://arxiv.org/abs/2008.03759).
 
 | Program | Complexity bound | Description |
@@ -45,4 +45,4 @@ All "alternate" variants use left/right and inverse change of basis (`*CoB*` fil
 **Benchmarks**:
 - `accuracy_2x2_real.m`: comparing algorithms accuracy
 - `accuracy_alternate_real.m`: comparing alternate change of basis
-- `gallery_alternate_real.m`: change of basis on large condition number
+- `gallery_alternate_real.m`: change of basis on large condition number

Strassen_CoB.m

@@ -1,6 +1,6 @@
 function M = Strassen_CoB(A, nmin)
 %          Left & Right change of basis of the sparsification
-%          of Strassen's algorithm via alternate basis.
+%          of Strassen's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

Strassen_ICoB.m

@@ -1,6 +1,6 @@
 function M = Strassen_ICoB(A, nmin)
 %          Inverse change of basis of the sparsification
-%          of Strassen's algorithm via alternate basis.
+%          of Strassen's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

Strassen_alternate.m

@@ -1,6 +1,6 @@
 function C = Strassen_alternate(A, B, nmin)
 %          Sparsification of Strassen's algorithm
-%          via alternate basis.
+%          via alternative basis.
 
 %          Reference:
 %          G. Beniamini, N. Cheng, O. Holtz, E. Karstadt, O. Schwartz;

Strassen_mul_alternate.m

@@ -1,6 +1,6 @@
 function C = Strassen_mul_alternate(A, B, nmin)
 %          Sparse multiplication of the sparsification
-%          of Strassen's algorithm via alternate basis.
+%          of Strassen's algorithm via alternative basis.
 
 if nargin < 3, nmin = 8; end
 

Winograd_CoB.m

@@ -1,6 +1,6 @@
 function M = Winograd_CoB(A, nmin)
 %          Left & Right change of basis of the sparsification
-%          of Winograd's algorithm via alternate basis.
+%          of Winograd's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

Winograd_ICoB.m

@@ -1,6 +1,6 @@
 function M = Winograd_ICoB(A, nmin)
 %          Inverse change of basis of the sparsification
-%          of Winograd's algorithm via alternate basis.
+%          of Winograd's algorithm via alternative basis.
 
 if nargin < 2, nmin = 8; end
 n = length(A);

Winograd_alternate.m

@@ -1,6 +1,6 @@
 function C = Winograd_alternate(A, B, nmin)
 %          Sparsification of Winograd's algorithm
-%          via alternate basis.
+%          via alternative basis.
 
 %          Reference:
 %          E. Karstadt, O. Schwartz; Matrix multiplication, a little faster.

Winograd_mul_alternate.m

@@ -1,6 +1,6 @@
 function C = Winograd_mul_alternate(A, B, nmin)
 %          Sparse multiplication of the sparsification
-%          of Winograd's algorithm via alternate basis.
+%          of Winograd's algorithm via alternative basis.
 
 if nargin < 3, nmin = 8; end