Area—time tradeoffs for matrix multiplication and related problems in VLSI models

Area-Time Tradeoff for Rectangular Matrix Multiplication in VLSI Models

Quantum Complexity of Boolean Matrix Multiplication and Related Problems

Complexity of Matrix Multiplication and Bilinear Problems

Algebraic complexity theory is the study of computation using algebraic models. One of the main achievements of this field has been the introduction of methods to prove lower bounds on the computational complexity, in algebraic models of computation, of concrete problems. Another major achievement has been the development of powerful techniques to construct fast algorithms for computational pro...

Optimal Matrix Multiplication on Fault-Tolerant VLSI Arrays

where h is the decision tree height, or the number of radial cuts, whose i cross edges can be chosen independently: h = (f L-k-l) / (f-1). Therefore, the number of permutations having the number of cross edges i = 1 in a stage-k subgraph of an (3, L) CC-banyan is C;,k=3(3L-k-1)/2, 0 < k < L-2. Now we can evaluate the total number of permutations in CC-banyan with fan-out 3. Theorem 6: The numbe...

Tradeoffs between Accuracy and Efficiency for Optimized and Parallel Interval Matrix Multiplication

Interval arithmetic is mathematically defined as set arithmetic. For implementation issues, it is necessary to detail the representation of intervals and to detail formulas for the arithmetic operations. Two main representations of intervals are considered here: inf-sup and midrad. Formulas for the arithmetic operations, using these representations, are studied along with formulas that trade of...