Approximation techniques for engineers

315 Pages·2007·1.55 MB·English

by  Louis Komzsik

APPROXIMATION
TECHNIQUES
for
ENGINEERS

APPROXIMATION
TECHNIQUES
FOR
ENGINEERS
Louis Komzsik
UGS Corp.
Cypress, California
Boca Raton London New York
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T&F_LOC_A_Master.indd 1 6/14/06 9:32:47 AM
To my wife, Gabriella

Preface
This book is a collection of methods that provide an approximate result for
certain engineering computations. The di(cid:11)erence from the analytical result
(if such exists at all) occurs due to the formulation chosen to execute a com-
putation. As such, it must be distinguished from numerical errors occurring
due to the computational round-o(cid:11)errorof the (cid:12)nite precision of computers.
Thereisaperennialquestbymathematiciansandengineersto(cid:12)ndapprox-
imate results in two classes of problems. In one class, the input data may
only be given by a discrete set of points to describe the continuous geometry
of a physical phenomenon; however, a continuous function (cid:12)tting the data is
sought. Itisalsopossibleinthisclassthattheinputdataisgivenbyfunctions
thatneedtobeapproximatedbyanotherfunctionorsomediscretequantities
ofthefunctions(suchasderivativeatcertainpoint)arerequired. Intheother
class, usually a continuous problem is posed and an approximate solution at
a discrete set of points is desired, forpracticalreasonssuch as computational
cost.
Accordingly, the book is divided into two parts: data approximation tech-
niques and approximate solutions. The (cid:12)rst part starts with the classical
interpolation methods, followed by spline interpolations and least square ap-
proximations. It also covers various approximations of functions as well as
their numerical di(cid:11)erentiation and integration. The second part ranges from
the solution of algebraic equations, linear and nonlinear systems, through
eigenvalue problems to initial and boundary value problems. Both parts em-
phasize the logical thread and common principles of the approximationtech-
niques.
The book is intended to be an everyday tool as a reference book for prac-
ticing engineers, researchers and graduate engineering students. It is hoped
thatthe readerscansolveaparticularapproximationproblemarisingintheir
practice by directly focusing on a chapter or section describing the appropri-
ate techniques.
Louis Komzsik
vii

Acknowledgments
Iwouldliketothankmycoworker,Dr.LeonardHo(cid:11)nungofUGS forhiscare-
fulmathematicalproofreadingandveri(cid:12)cationofthecomputationalexamples
whilerepresentingasoftwareengineer’sperspective. Ialsoappreciatethecom-
mentsandrecommendationsofDr.JonathanHartofNorthrop-GrummanCor-
poration, whoalso veri(cid:12)edthe mathematical details andreadthe manuscript
with the eye of the application engineer.
Manythanksareduetothegreatsta(cid:11)ofTaylorandFrancisBooks. Specif-
ically, I would like to acknowledge the most enthusiastic support from Nora
Konopka, publisher and Helena Redshaw, manager. I am grateful for very
valuable corrections and contributions from Gloria Goss, proofreader and
Michael Davidson, editor.
Louis Komzsik
ThemodelinthecoverartisbycourtesyofDaimlerChryslerCorporation.
The rendering is intended to illustrate the wide-spread use of approximation
techniques. The engineering audience and the engineering applications are
represented by the car model. In addition, biological and environmental sci-
ences, depicted by the human and the road models, also frequently use the
approximation techniques of this book.
ix