On an algorithm converging to hyperstochastic tensors.

A nonnegative tensor I A i is I hyperstochastic i if Graph HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>=</mo><mn>1</mn></math> ht for all I i i , I j i . Let Graph HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mrow><msub><mi>i</mi><mn>1</mn></msub><mo>...</mo><msub><mi>i</mi><mi>k</mi></msub></mrow></msub><msub><mo stretchy="false">)</mo><mrow><mn>1</mn><mo><=</mo><msub><mi>i</mi><mn>1</mn></msub><mo>,</mo><mo>...</mo><mo>,</mo><msub><mi>i</mi><mi>k</mi></msub><mo><=</mo><mi>N</mi></mrow></msub><mo> </mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mrow><mi>N</mi><mo>×</mo><mo>---</mo><mo>×</mo><mi>N</mi></mrow></msup></math> ht be a I k i -tensor. For Graph HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo><=</mo><mi>j</mi><mo><=</mo><mi>k</mi></math> ht and Graph HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo><=</mo><mi>i</mi><mo><=</mo><mi>N</mi></math> ht , we denote by Graph HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>=</mo><munderover><mo> </mo><mrow><msub><mi>i</mi><mn>1</mn></msub><mo>,</mo><mo>...</mo><mo>,</mo><msub><mi>i</mi><mrow><mi>j</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>i</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><mo>...</mo><mo>,</mo><msub><mi>i</mi><mi>k</mi></msub><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><msub><mi>a</mi><mrow><msub><mi>i</mi><mn>1</mn></msub><msub><mi>i</mi><mrow><mi>j</mi><mo>-</mo><mn>1</mn></mrow></msub><mi>i</mi><msub><mi>i</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>...</mo><msub><mi>i</mi><mi>k</mi></msub></mrow></msub></math> ht the sum of the I i i th slice in the I j i th direction. [Extracted from the article]