Lectures on the Complexity of Bilinear Problems

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Springer Science & Business Media, Feb 23, 1987 - Computers - 135 pages
 

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Contents

I Complexity and rank of bilinear mappings
7
I2 How much divisions can help
9
I3 Computations complexity and rank of bilinear mappings
15
II Elementary properties of rank and approximate rank of bilinear mappings
26
simple lower bounds using tensor slices
33
II3 Direct products sums of bilinear mappings the ordinary and the extended rank conjecture
35
II4 Tensor products of bilinear mappings
41
II5 Algorithmic equivalence of bilinear problems
43
III2 The T theorem
64
III3 Further applications of the Ttheorem
75
IV Complexity and rank of finite dimensional associative algebras
83
IV 2 The theorem of Alder and Strassen
86
IV 3 Algebras of minimal rank
95
V Algorithm varieties
111
V2 Some special algorithm varieties
118
References
129

II6 Border rank of bilinear mappings
46
III Multiplication of large matrices
57

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