Computational complexity and numerical stability

Authors:
Webb Miller
Affiliations:
-
Venue:
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Year:
1974

Citing 5
Cited 1

Numerical methods with Fortran IV case studies

Numerical methods with Fortran IV case studies
On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives

Journal of the ACM (JACM)
Computer Approximations

Computer Approximations
Algorithms for matrix multiplication

Algorithms for matrix multiplication
Rounding Errors in Algebraic Processes

Rounding Errors in Algebraic Processes

Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product

IEEE Transactions on Computers

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Abstract

Limiting consideration to algorithms satisfying various numerical stability requirements may change lower bounds for computational complexity and/or make lower bounds easier to prove. We will show that, under a sufficiently strong restriction upon numerical stability, any algorithm for multiplying two n×n matrices using only +, − and × requires at least n3 multiplications. We conclude with a survey of results concerning the numerical stability of several algorithms which have been considered by complexity theorists.