## Error-free computation: why it is needed and methods for doing it |

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0bviously arithmetic operations automatic digital computer base vector called Cauchy sequence Chapter close to f(d coefficients commutative ring computational algorithms condition number Corollary correct answer decimal defined division divisor elements of F error analysis exists exponent Farey fraction finite field finite-segment p-adic arithmetic floating-point arithmetic floating-point Hensel code Gaussian elimination Hence ill-conditioned problem least common multiple linear algebraic linear algebraic equations mantissa mapping matrix matrix norm maximum norm metric space mixed-radix digits multiple-modulus residue arithmetic multiplicative inverses modulo n-tuple non-zero normalized floating-point Hensel numerical mathematician numerical mathematics numerically stable obtain ordinary Hensel code p-adic expansion p-adic metric p-adic numbers p-adic point p-adic units partial remainder pivot positive integer radix fraction rational numbers real number system relatively prime Remark residue digits residue number system result modulo rounding errors scaling significant digits single-modulus residue arithmetic standard residue representation subtraction symmetric residue Theorem Wilkinson write Young and Gregory zero