## On Prony's method of fitting exponential decay curves and multiple-hit survival curves |

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accuracy adjusted values Ai+1 algebraic equation approximation Atomic Energy Commission calculate Carbide and Carbon CARBON CHEMICALS DIVISION choose coefficients column vector components COMPUTING consists in solving correct method criterion for determining determining the number difference equation document equation of order equations 16 experimental values exponentials required FITTING EXPONENTIAL DECAY Hence invert least squares fit linear combination linear equations linearly measurements METHOD OF FITTING method or process MULTIPLE-HIT SURVIVAL CURVES multipliers n-th normal equations number of exponentials OAK RIDGE obtain a valid Operated by Carbide ordinary least squares orthogonal place of 9 proceed as follows process disclosed Prony's method pseudo-normal equations quantities rename satisfied a difference sequentially smaller number solution solve the algebraic statistical weights step consists strictly subject to error thereafter triangular matrix valid least squares vanish vectors vQ Whittaker and Robinson Willers