Optimization Using Personal Computers
With Applications to Electrical Networks
John Wily and Sons 1987
Thomas R. Cuthbert Jr., his second book, and he is now
Director, Digital Signal Processing
Collins Transmission System Division
Rockwell International Corporation
Dallas Texas
Thomas Remy Cuthbert, born 1928
Now this book, like his prior, has a really stupid title. But never mind the math in this is really good and I have long wanted to read it.
Cuthbert has got a card in the book where in 1987 you could send $30 to Wiley and get a 5 1/4 DSDD floppy with all 33 of the BASICA programs, plus some test data.
Lots of references, but different from his other book.
Curtbert gives refences for Problem matrices, not maybe singular, but still problematic, and for other data too.
first of all Knuth 1968, Art of Computer Programming. And matrix types, Vandermonde, Combinatorial, Cauchy, Hilbert
and then Nash 1979 Compact Numerical Methods for Computers: Linear Algebra and Function Administration
matrix types: Hilbert, Ding Dong, Moler, Bordered, Diagonal, Wilkinson W+, Ones
Dongarra, J. J., C B. Moler etal (1979) LINPACK User's Guide, SIAM
Smith (1976) and Garbow (1977) document the EISPACK eigensystem
Hopper (1981) Harwell Subroutine Library. United Kingdom Atomic Energy Authority
Compact numerical methods for computers : linear algebra and function minimisation / J.C. Nash. (1990 2nd edition)
*
So this seems to be a pivotal reference,
Smith, Boyle, Dongarra, Garbow, Ikebe, Kelma etal
Matrix Eigensystem Routines, Springer-Verlag, 1976
Matrix eigensystem routines : EISPACK guide / B. T. Smith [and others] 1976
*
also available is a 1977 extension guide
And Cuthbert's book:
Optimization Using Personal Computers: With Applications to Electrical Networks Hardcover – January 1, 1987
by Thomas R. Cuthbert
Courant, R. (1936) Differential and Integral Calculus, Wiley
Differential and integral calculus / by R. Courant ; translated by E. J. McShane. (1937 2nd edition)
*
And he has other books too.
I like old books like this because I can see how they likely explained things differently.
Continuing with Cuthbert:
Optimization Using Personal Computers
With Applications to Electrical Networks
John Wily and Sons 1987
Cuthbert p14
He sites:
Acton, F. S. (1970) Numerical Methods That Work
Numerical methods that work / Forman S. Acton. (Mathematical Association of America 1990)
* widely disseminated
Cuthbert quotes Acton:
"
minimum-seeking methods are often used when a modicum of thought would disclose more appropriate techniques. They are the first refuge of the computational scoundrel, and one feels at times that the world would be a better place if they were quietly abandoned. ... The unpleasant fact that the approach can well require 10 to 100 times as much computation as methods more specific to the problem is ignored -- for who can tell what is being done by the computer?
"
I have seen this first hand. Curthbert is writing in 1987. A lot of this correlates to the popularity of personal computers and to the rise of some software vendors who's names I will not speak.
They promote idiocy. And wasting computer cycles is not by itself that important. The problem is that the entire approach to the problem at hand is completely wrong headed. And then the simulation program becomes a child's busy box, a video game. And the well paid people who are running this are just glorified script files. The simulation program serves as a division of labor, as there will be one pit boss who gives the orders, and then minions who carry it out. Very very little smarts is being used, and what results is usually completely appropriate, but they will never understand this.
I am embarrassed to admit that I know how many millions of dollars a company can blow through doing this. And I know there are large sectors of industry which are entirely like this.
I have seen things like this in human behavior all along. But this specific kind of stuff pertaining to computer simulations I first learned of reading discussion way way back about the race for the 64k DRAM chips. The US firms lost and Japan won. One analysis explained that in the US modelling and simulations some wrong assumptions had been made. But 95% of those doing the design and simulations were not even aware that there were such assumptions.
These people, they just know that if they continue being good frat boys, then they will continue to get paid and continue to have social approval. This is about all they are good for. They understand things in terms of buzz words, but they don't have an in depth understanding of how the ideas developed, what really is at issue, or of what the limitations are in the analysis. They don't understand the assumptions behind the buzz words.
So continuing on with Thomas Remy Cuthbert jr. 1987
So he gives us a function F in the variables x and y. So he shows a graph of F rising over the x and y plane. There are 4 local maxima and 3 saddle points.
The function he gives us in that that complex, but it seems to be just an example to give us the idea.
So he talks about partial derivates and then he talks about approximating the maxima by a parabola in two variables.
Not sure why you really need to do this here, and he does not go into the math to do this, but he has 33 BASICA programs to do it.
I think if the function F were something for which each point required lengthy simulations, then by using the 2d parabolic approximation you might be able to get a satisfactory result more quickly.
Himmelblau, D. M. (1972) Applied Nonlinear Programming, McGraw Hill
Applied nonlinear programming [by] David M. Himmelblau (1972)
*
Himmelblau has other books oriented towards numerics for Chemical Engineering.
And Nonlinear Programming is the description of all this preferred by Cuthbert.
Gilbert Strang, Linear Algebra 1976, read just a couple of months ago.
And Cuthbert idenfies himself as being with Collins Radio Company, Texas Instruments, and Rockwell International and he signs his preface as being in Plano Texas.
He acknowledges Karl R. Varan. Our local Varian?
Davidson, W. C. (1959) wrote books about this, but not standard publishing.
In 1847 Cauchy described the method of steepest ascent.
Traub, J. F. (1964) Iterative Method for the Solution of Equations
Iterative methods for the solution of equations / [by] J.F. Traub. (1964)
*
and also note:
Information, uncertainty, complexity / J.F. Traub, G.W. Wasilkowski, H. Woźniakowski (1983)
*
Lootsman, F. A. (1972) Numerical Methods for Nonlinear Optimization
Numerical methods for non-linear optimization : Conference sponsored by the Science Research Council, University of Dundee, Scotland, 1971 / Edited by F. A. Lootsma.
* a conference digest
Vlach J. and K. Singhal(1983) Computer Methods for Circuit Analysis and Design
Computer methods for circuit analysis and design / Jiří Vlach, Kishore Singhal (1983)
*
Dixon, L. C. W. (1972) Nonlinear Optimization
0
Practical methods of optimization / R. Fletcher (1980) 2 volumes
*
Selected applications of nonlinear programming / [by] Jerome Bracken and Garth P. McCormick.
Imprint New York : Wiley, [1968]
*
Compact numerical methods for computers : linear algebra and function minimisation / J.C. Nash. (1990 second edition)
*
Methods for solving systems of nonlinear equations / Werner C. Rheinboldt (1998 2nd ed)
*
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