Error analysis of linear recursions in floating point

A stochastic error model for floating point arithmetic is developed and used to study the effects of finite wordlength on linear recursive formulas. Optimal realizations exist, but they are highly sensitive.

[1]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[2]  Paul Moroney,et al.  Issues in the implementation of digital feedback compensators , 1983 .

[3]  David W. Matula,et al.  A Simulative Study of Correlated Error Propagation in Various Finite-Precision Arithmetics , 1973, IEEE Transactions on Computers.

[4]  Erik I. Verriest.  On redefining the optimal least squares filter under floating point operations , 1984, ICASSP '84. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[5]  G. Stewart.  Introduction to matrix computations , 1973 .

[6]  Gain correction in optimal filtering using floating point arithmetic , 1984, The 23rd IEEE Conference on Decision and Control.

[7]  Ulrich W. Kulisch,et al.  Mathematical Foundation of Computer Arithmetic , 1977, IEEE transactions on computers.

[8]  W. Koning,et al.  The influence of finite word length on digital optimal control , 1984 .

[9]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[10]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[11]  J. Aggarwal,et al.  Error analysis of digital filter employing floating-point arithmetic , 1971 .

[12]  R. Rink,et al.  Performance of state regulator systems with floating-point computation , 1979 .

[13]  R. P. Brent,et al.  On the Precision Attainable with Various Floating-Point Number Systems , 1972, IEEE Transactions on Computers.

[14]  Xiaomei Yang.  Rounding Errors in Algebraic Processes , 1964, Nature.

[15]  A. Sripad,et al.  A necessary and sufficient condition for quantization errors to be uniform and white , 1977 .

[16]  James S. Vandergraft,et al.  Introduction to Numerical Computations , 1983 .

[17]  Richard P. Brent.  On the Precision Attainable with Various Floating-Point Number Systems , 1973, IEEE Trans. Computers.