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Page 2511 of Mathematical Reviews Vol. , Issue 83f
[page]

1983
*
Mathematical Reviews
*

This very important paper shows how to replace

*some**of**the**intervals*occurring*in**the**interval**arithmetic*version*of*Newton’s method by reals. ...*The**problem*is transformed to a nonlinear system*of*simultaneous equations which allows*one*to apply*the*well-known*interval**arithmetic*version*of*Newton’s method. G. Alefeid (Karlsruhe) ...##
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Interval Mathematics Techniques for Control Theory Computations
[chapter]

1989
*
Computation and Control
*

*In*both, we define

*interval*

*arithmetic*

*on*

*complex*numbers by identifying a

*complex*intervalc with an ordered pair (a, b)

*of*real

*intervals*; we then define

*complex*

*interval*

*arithmetic*by extending

*the*standard ...

*In*particular,

*interval*methods can find, with

*the*rigor

*of*a mathematical proof, even

*on*a computer, all roots

*of*a function

*in*

*the*right half

*of*

*the*

*complex*plane. ...

##
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Page 5649 of Mathematical Reviews Vol. , Issue 93j
[page]

1993
*
Mathematical Reviews
*

Us- ing circular

*complex**interval**arithmetic*, we study*the*dependence*of**the*convergence rate*of*root-finding algorithms*on*errors origi- nating from*the*rounding as well as*the*approximate computations ...*In*addition to real n x n point matrices, we consider*complex*matrices,*interval*matrices and*the*generalized eigenvalue*problem*.” ...##
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Page 8727 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

Best approximation

*problems*for*some*elementary*problems*are treated*in*Chapter 3. ...*In*summary, it can be said that*the*book belongs*on**the*desk*of*every researcher who is using val- idation numerics*in**the**complex*field. G. ...##
###
Review of introduction to interval computations, by Götz Alefeld and Jürgen Herzberger

1986
*
Linear Algebra and its Applications
*

*of*

*interval*

*arithmetic*available

*in*

*the*past. ... Furthermore, strides have been made

*in*advance

*of*

*the*implementation

*of*

*the*standard

*in*efficient support for

*interval*

*arithmetic*. ...

*The*book covers

*the*fundamentals

*of*real and

*complex*

*interval*

*arithmetic*, methods for finding

*intervals*containing zeros

*of*real functions and real and

*complex*roots

*of*polynomials, methods based

*on*iteration ...

##
###
Why does information-based complexity use the real number model?

1999
*
Theoretical Computer Science
*

This model has been used

doi:10.1016/s0304-3975(98)00300-4
fatcat:bypyiuafj5cwriyzg2c3rl6jba
*in*algebraic*complexity*already*in**the*1950s*in**the*work*of** ... We also indicate*the*possible tradeoffs between*complexity*and stability, and*the*need*of*using multiple or varying precision for ill-conditioned*problems*. ... Acknowledgements I thank Erich Novak, Leszek Plaskota, Joseph Traub, Grzegorz Wasilkowski and Arthur Werschulz for many valuable comments*on*this paper. ...##
###
Page 400 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

Together with an

*interval*residual*arithmetic*,*some*function evaluation examples are included. This is a fine paper for newcomers*in**the*field. {For*the*entire collection see MR 91k:00034.} E. ... Summary: “Newton’s method is usually considered*on*R. But A. Cayley investigated a*complex*version*in**the*‘Newton-Fourier imaginary*problem*’. ...##
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Page 535 of Mathematical Reviews Vol. , Issue 97A
[page]

1997
*
Mathematical Reviews
*

Markov,

*On**the*foundations*of**interval**arithmetic*(307-313); Yurii 1. Shokin [Yu. I. ... Lakeev] and Jifi Rohn, Computational*complexity**of**interval*algebraic*problems*:*some*are feasible and*some*are computation- ally intractable—a survey (293-306); Svetoslav M. ...##
###
Midpoint-radius interval-based method to deal with uncertainty in power flow analysis

2017
*
Electric power systems research
*

This paper presents a novel method based

doi:10.1016/j.epsr.2017.02.017
fatcat:2e62zqkmjjbohj4fyb7dmkxtqq
*on*midpoint-radius*interval**arithmetic*to deal with uncertainties*in**the*power ow*problem*. ... Moreover,*the*proposed formulation is combined with an optimisation*problem**in*order to prevent overestimation*of**the**interval*solution while preserving uncertainty. ... This can become a major issue to*the*application*of**interval**arithmetic*to real-world*problems*, especially to non-linear*ones*. ...##
###
Page 739 of Mathematical Reviews Vol. , Issue 83b
[page]

1983
*
Mathematical Reviews
*

ISBN 0-12-428650-X This book is concerned with

*arithmetic**in**the*spaces*of*numerical computation—including real and*complex*numbers,*intervals*,*complex**intervals*, and vectors and matrices with such components—and ...*The*author discusses*the*following*problem*:*One*is given a computational algorithm P which may be defined*in**some*programming language, e.g. ALGOL 60. ...##
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"COMMONSENSE" ARITHMETIC REASONING
[chapter]

1990
*
Readings in Qualitative Reasoning About Physical Systems
*

*Arithmetic*reasoning" can range

*in*

*complexity*... Figure 4 presents

*some*

*of*

*the*operators used by Quantity Lattice

*in*doing

*interval*

*arithmetic*.' ... Introduction "Cogito Ergo Sum" -I think, therefore I add "

*Arithmetic*reasoning" denotes a broad class

*of*inferences which range

*in*

*complexity*from simple integer

*arithmetic*, such as "l+ 1 = 2," to

*complex*...

##
###
Page 5409 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

*Interval*

*arithmetic*and

*interval*standard functions are needed

*in*searching for self-validating methods

*of*numerical solution

*of*mathematical

*problems*. ...

*In*practice, computer

*arithmetic*(

*in*

*the*system S

*of*float- ing point numbers) must be used instead

*of*(real)

*arithmetic*(

*on*R). ...

##
###
An introduction to the scientific computing language Pascal-SC

1987
*
Computers and Mathematics with Applications
*

Its most important features are: (i) accurate floating-point

doi:10.1016/0898-1221(87)90181-7
fatcat:5kaukwfwybalho2o27zqi6mwei
*arithmetic*for real,*complex*, and*interval*numbers, vectors, and matrices, with controlled rounding if desired; (ii)*the*convenience*of*operator ... These basic features*of*Pascal-SC will be described, together with*some*applications. ... Acknowledgements--*The*author would like to thank Professor George F. Corliss for reading*the*manuscript carefully, and a large number*of*valuable suggestions. ...##
###
Page 2847 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

Summary: “

*In*this note we give*some*comments*on*recent results concerning a simultaneous method*of*fourth order for finding*complex*zeros*in*circular*interval**arithmetic*. ... A direct*interval**arithmetic*evaluation*of*a formula for*the*function yields*in*general a superset with an error linear*in**the*width*of**the**interval*. ...##
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Extending the Range of C-XSC: Some Tools and Applications for the Use in Parallel and Other Environments
[chapter]

2009
*
Lecture Notes in Computer Science
*

An example

doi:10.1007/978-3-642-01591-5_6
fatcat:m5uiqt3sqffbthl7rjygmvq6qe
*of*this is presented for*the*Maple*interval*package intpakX. ... Different versions*of*parallel verified linear system solvers based*on**the*package are now available. ... -*Arithmetic*Extensions -C-XSC*The*C-XSC Hansen*Arithmetic*which represents a generalized*interval**arithmetic*has also been developed lately*in**the*course*of**the*development*of*a parametric*interval*linear ...
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