Error-free Computation: Why it is Needed and Methods for Doing it |
Common terms and phrases
arithmetic operations automatic digital computer B₁ B₂ base vector called Cauchy sequence Chapter coefficients commutative ring condition number Corollary correct answer d₁ D₂ decimal defined division divisor elements of F error analysis example exists exponent Farey fraction finite-segment p-adic arithmetic floating-point arithmetic floating-point Hensel code Gaussian elimination Hence ill-conditioned problem lalm least common multiple linear algebraic linear algebraic equations m₁ m₂ mantissa mapping matrix maximum norm metric space mixed-radix digits modulo multiple-modulus residue arithmetic multiplicative inverse n-tuple non-zero normalized floating-point Hensel numerical mathematician numerical mathematics numerically stable numerically unstable algorithm obtain ordinary Hensel code p-adic expansion p-adic metric p-adic numbers p-adic point p-adic units pivot positive integer r₁ radix radix fraction radix-5 rational numbers real number system relatively prime Remark residue digits residue number system result modulo rounding errors significant digits single-modulus residue arithmetic standard residue representation subtraction symmetric residue t₂ Theorem Wilkinson write Young and Gregory zero