This article discusses several erroneous claims which appear in textbooks on numerical methods and computational physics. These are not typos or mistakes an individual author has made, but widespread misconceptions. In an attempt to stop these issues from further propagating, we discuss them here, along with some background comments. In each case, we also provide a correction, which is aimed at summarizing material that is known to experts but is frequently mishandled in the introductory literature. To make the mistakes and corrections easy to understand, we bring up specific examples drawn from elementary physics and math. We also take this opportunity to provide pointers to the specialist literature for readers who wish to delve into a given topic in more detail.

1.
A.
Gezerlis
,
Numerical Methods in Physics with Python
(
Cambridge U. P.
,
Cambridge
,
2020
).
2.
F. S.
Acton
,
Numerical Methods That Work
(
The Mathematical Association of America
,
Washington, D.C.
,
1990
).
3.
U. M.
Ascher
and
C.
Greif
,
A First Course in Numerical Methods
(
Society for Industrial and Applied Mathematics
,
Pennsylvania
,
2011
).
4.
J. F.
Boudreau
and
E. S.
Swanson
,
Applied Computational Physics
(
Oxford U. P.
,
Oxford
,
2018
).
5.
R. L.
Burden
,
D. J.
Faires
, and
A. M.
Burden
,
Numerical Analysis
, 10th ed. (
Cengage Learning
,
Massachusetts
,
2015
).
6.
G.
Dalhquist
and
Å.
Björck
,
Numerical Methods
(
Prentice-Hall
,
New Jersey
,
1974
).
7.
J.
Franklin
,
Computational Methods for Physics
(
Cambridge U. P.
,
Cambridge
,
2013
).
8.
A. L.
Garcia
,
Numerical Methods for Physics
(
CreateSpace
,
California
,
2017
).
9.
N. J.
Giordano
and
H.
Nakanishi
,
Computational Physics
, 2nd ed. (
Pearson
,
London
,
2005
).
10.
A.
Gilat
and
V.
Subramaniam
,
Numerical Methods for Engineers and Scientists
, 3rd ed. (
Wiley
,
New Jersey
,
2013
).
11.
H.
Gould
,
J.
Tobochnik
, and
W.
Christian
,
An Introduction to Computer Simulation Methods
, Rev. 3rd ed. (
CreateSpace
,
California
,
2017
).
12.
R. W.
Hamming
,
Numerical Methods for Scientists and Engineers
, 2nd ed. (
McGraw-Hill
,
New York
,
1973
).
13.
M. T.
Heath
,
Scientific Computing
, 2nd ed. (
McGraw-Hill
,
New York
,
2002
).
14.
J. D.
Hoffman
,
Numerical Methods for Engineers and Scientists
, 2nd ed. (
Marcel Dekker
,
New York
,
2001
).
15.
J.
Izaac
and
J.
Wang
,
Computational Quantum Mechanics
(
Springer
,
Berlin
,
2018
).
16.
J.
Kiusalaas
,
Numerical Methods for Engineers with Python 3
(
Cambridge U. P.
,
Cambridge
,
2013
).
17.
A.
Klein
and
A.
Godunov
,
Introductory Computational Physics
(
Cambridge U. P.
,
Cambridge
,
2006
).
18.
S.
Koonin
and
D. C.
Meredith
,
Computational Physics
(
Addison-Wesley
,
Massachusetts
,
1990
).
19.
R. H.
Landau
,
M. J.
Páez
, and
C. C.
Bordeianu
,
Computational Physics
, 3rd ed. (
Wiley-VCH
,
New Jersey
,
2015
).
20.
M.
Newman
,
Computational Physics
, Rev. ed. (
CreateSpace
,
California
,
2012
).
21.
P.
Olver
and
C.
Shakiban
,
Applied Linear Algebra
, 2nd ed. (
Springer
,
Berlin
,
2018
).
22.
T.
Pang
,
An Introduction to Computational Physics
, 2nd ed. (
Cambridge U. P.
,
Cambridge
,
2006
).
23.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in Fortran
, 2nd ed. (
Cambridge U. P.
,
Cambridge
,
1992
).
24.
S.
Širca
and
M.
Horvat
,
Computational Methods in Physics
, 2nd ed. (
Springer
,
Berlin
,
2018
).
25.
Institute of Electrical and Electronics Engineers 754 Standard for Binary Floating-Point Arithmetic
(
1985
).
26.
W.
Kahan
, “
The improbability of probabilistic error analysis
,” in
Third ICIAM Congress
(
1995
).
27.
N. J.
Higham
,
Accuracy and Stability of Numerical Algorithms
, 2nd ed. (
Society for Industrial and Applied Mathematics
,
Pennsylvania
,
2002
), pp.
25
26
.
28.
J. H.
Wilkinson
,
The Algebraic Eigenvalue Problem
(
Oxford U. P.
,
Oxford
,
1965
).
29.
L. N.
Trefethen
and
D.
Bau
 III
,
Numerical Linear Algebra
(
Society for Industrial and Applied Mathematics
,
Pennsylvania
,
1997
).
30.
L. N.
Trefethen
,
Approximation Theory and Approximation Practice
(
Society for Industrial and Applied Mathematics
,
Pennsylvania
,
2012
), pp.
39
49
.
31.
R. M.
Martin
,
L.
Reining
, and
D. M.
Ceperley
,
Interacting Electrons: Theory and Computational Approaches
(
Cambridge U. P.
,
Cambridge
,
2016
), p.
583
.
32.
G. O.
Roberts
,
A.
Gelman
, and
W. R.
Gilks
, “
Weak convergence and optimal scaling of random walk metropolis algorithms
,”
Ann. Appl. Probab.
7
,
110
120
(
1997
).
33.
T.
Judt
and
T.
Snyder
,
Thinking the Twentieth Century
(
The Penguin Press
,
London
,
2012
), p.
267
.
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