Sensitivity Analysis in Linear Systems ©
01-01-2020, 06:01 PM
Post: #1
 SlideRule Senior Member Posts: 1,301 Joined: Dec 2013
Sensitivity Analysis in Linear Systems ©
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!
SlideRule
01-03-2020, 08:56 AM
Post: #2
 Ángel Martin Senior Member Posts: 1,246 Joined: Dec 2013
RE: Sensitivity Analysis in Linear Systems ©
Thanks for this one, but I miss the link to the actual article... was it meant to be included?
01-03-2020, 12:56 PM
Post: #3
 PedroLeiva Member Posts: 178 Joined: Jun 2014
RE: Sensitivity Analysis in Linear Systems ©

Pedro
01-03-2020, 12:58 PM (This post was last modified: 01-03-2020 12:58 PM by SlideRule.)
Post: #4
 SlideRule Senior Member Posts: 1,301 Joined: Dec 2013
RE: Sensitivity Analysis in Linear Systems ©
(01-03-2020 08:56 AM)Ángel Martin Wrote:  Thanks for this one, but I miss the link to the actual article... was it meant to be included?

The post was merely a reference {sans link}, sorry.

SlideRule

ps: thanks Pedro.
01-04-2020, 07:08 AM
Post: #5
 Ángel Martin Senior Member Posts: 1,246 Joined: Dec 2013
RE: Sensitivity Analysis in Linear Systems ©