01-01-2020, 06:01 PM

Excerpts from Sensitivity Analysis in Linear Systems, © Springer-Verlag Berlin Heidelberg 1986, ISBN-13:978-3-642-82741-9, e-ISBN-13:978-3-642-82739-6

pg. 9 1.3 Condition Number and Nearness to Singularity

For instance, a matrix A of order n processed on an HP-15C calculator - having a ten-digit mantissa - has an error ││ΔA││ less than 5 x 10⁻¹° x n ││ΔA││ (i.e. less than 10⁻⁹ n││ΔA││).

pg. 11 1.3 Condition Number and Nearness to Singularity

To investigate how the condition number can give a measure of nearness to singularity, we will borrow the following example from the HP-15C advanced matrix functions library.

pg. 28 1. Perturbation of Linear Equations

Therefore, for any vector b, the solution must be expected to be only at accurate as the machine itself. Indeed, the choice of b … and the solution of the system on an HP-15C calculator with floating-point arithmetic yields …

pg. 30 I. Perturbation of Linear Equations

that Gauss elimination is not asymptotically stable for any pivotal strategy depending only on the coefficient matrix A. This is visualized by trying to solve Ax = b in Hamming's example on an HP-15C calculator with floating-point arithmetic and a ten-digit accuracy.

…

…Solving the scaled equations … on an HP-15C for …

BEST!

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pg. 9 1.3 Condition Number and Nearness to Singularity

For instance, a matrix A of order n processed on an HP-15C calculator - having a ten-digit mantissa - has an error ││ΔA││ less than 5 x 10⁻¹° x n ││ΔA││ (i.e. less than 10⁻⁹ n││ΔA││).

pg. 11 1.3 Condition Number and Nearness to Singularity

To investigate how the condition number can give a measure of nearness to singularity, we will borrow the following example from the HP-15C advanced matrix functions library.

pg. 28 1. Perturbation of Linear Equations

Therefore, for any vector b, the solution must be expected to be only at accurate as the machine itself. Indeed, the choice of b … and the solution of the system on an HP-15C calculator with floating-point arithmetic yields …

pg. 30 I. Perturbation of Linear Equations

that Gauss elimination is not asymptotically stable for any pivotal strategy depending only on the coefficient matrix A. This is visualized by trying to solve Ax = b in Hamming's example on an HP-15C calculator with floating-point arithmetic and a ten-digit accuracy.

…

…Solving the scaled equations … on an HP-15C for …

BEST!

SlideRule