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Computational Functional Analysis Second Edition
Ramon E Moore Digital Instant Download
Author(s): Ramon E Moore, Michael J Cloud
ISBN(s): 9781904275244, 1904275249
Edition: Second Edition
File Details: PDF, 8.30 MB
Year: 2007
Language: english

COMPUTATIONAL FUNCTIONAL
ANALYSIS
Second Edition
"Although interval analysis is in a sense just a new language for inequalities, it is
a very powerful language and is one that has direct applicability to the important
problem of significance in large computations." - R.D. Richtmyer

ABOUT THE AUTHORS
Ramon E. Moore was Professor of Computer and Information Science at
Ohio State University until 2000. Formerly he had been Professor of
Mathematics at the University of Texas at Arlington; Professor of
Computer Sciences at the University of Wisconsin-Madison; Visiting
Professor, Freiburg University (Germany); Visiting Professor, Karlsruhe
University (Germany); Visiting Professor at the University of Oxford;
Visiting Professor at the Royal Institute of Technology (Sweden);
Associate Professor at the University of Wisconsin; and Applied
Mathematician with Lockheed in California from 1956-64. He is a
Member of the Society for Industrial and Applied Mathematics, and was
awarded the Alexander von Humboldt Foundation U.S. Senior Scientist
Award in 1975. He has written four previous books.
Michael J. Cloud is Associate Professor of Electrical and Computer
Engineering at Lawrence Technological University. He received BS and
MS degrees from Michigan State University, where he also obtained his
PhD in addition to holding the Dean's Distinguished Fellowship.
He is a Senior Member of the Institute of Electrical and Electronics
Engineers and has co-authored six previous books.

COMPUTATIONAL FUNCTIONAL
ANALYSIS
Second Edition
Ramon E. Moore
Professor of Computer and Information Science
Ohio State University
Michael J. Cloud
Associate Professor of Electrical and Computer Engineering
Lawrence Technological University, Michigan
Horwood Publishing
Chichester, UK

First edition published in 1984 by
ELLIS HORWOOD LIMITED
Second edition published in 2007 by
HORWOOD PUBLISHING LIMITED
International Publishers in Science and Technology
Coll House, Westergate, Chichester, West Sussex, PO20 3QL UK
© R.E.Moore & M.J.Cloud 2007. All Rights Reserved. No part of this
publication may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, photocopying, recording, or
otherwise, without the permission of Horwood Publishing, Coll House,
Westergate, Chichester, West Sussex, PO20 3QL, UK.
British Library Cataloguing in Publication Data
A catalogue record of this book is available from the British Library
ISBN-10: 1-904275-24-9
ISBN-13: 978-1-904-275-24-4
Printed and bound in the UK by Antony Rowe Limited.

Table of Contents
Preface vii
Notation ix
Chapter 1 Introduction 1
Chapter 2 Linear Spaces 3
linear manifolds; isomorphic spaces; Cartesian products; equivalence
classes; factor spaces
Chapter 3 Topological Spaces 7
convergent sequences; compactness; relative compactness; sequen
tial compactness; continuous functions; inverse mappings; homeomor-
phisms
Chapter 4 Metric Spaces 11
metrics; isometries; Cauchy sequences; completeness; dense subsets;
separable metric spaces; completion of a metric space
Chapter 5 Normed Linear Spaces and Banach Spaces 15
norms; bounded subsets; Banach spaces; subspaces
Chapter 6 Inner Product Spaces and Hilbert Spaces 19
Inner products; Cauchy-Schwarz inequality; orthogonality; E" and h
Hilbert spaces; JZ2[a,b] and h unit vectors; orthonormal sequences;
complete orthonormal sequences; separable Hilbert spaces; span of a
subset; orthogonal projections; orthogonal complements; orthonormal
bases; Parseval's identity and relation; Fourier coefficients; the Gram-
Schmidt process

VI Table of Contents
Chapter 7 Linear Functionals 28
functionals; linear functionals; bounded linear functionals; evaluation
functionals; finite sums; definite integrals; inner products; the Riesz
representation theorem; null spaces; norms; the Hahn-Banach theo
rem; unbounded functionals; conjugate (dual) spaces
Chapter 8 Types of Convergence in Function Spaces 32
strong convergence; weak convergence; pointwise convergence; uni
form convergence; star convergence; weak-star convergence
Chapter 9 Reproducing Kernel Hubert Spaces 35
reproducing kernels; orthogonal projection; interpolation; approximate
integration
Chapter 10 Order Relations in Function Spaces 42
reflexive partial orderings; intervals; interval valued mappings into
reflexively partially ordered sets; lattices; complete lattices; order
convergence; united extensions; subset property of arbitrary map
pings; the Knaster-Tarski theorem; fixed points of arbitrary map
pings; line segments in linear spaces; convex sets; convex mappings
Chapter 11 Operators in Function Spaces 49
operators; linear operators; nonlinear operators; null spaces; non-
singular linear operators; continuous linear operators; bounded lin
ear operators; Neumann series and solution of certain linear opera
tor equations; adjoint operators; selfadjoint operators; matrix repre
sentations of bounded linear operators on separable Hubert spaces;
the space L(H,H) of bounded linear operators; types of convergence
in L(H,H); Jacobi iteration and Picard iteration; linear initial value
problems
Chapter 12 Completely Continuous (Compact) Operators 60
completely continuous operators; Hilbert-Schmidt integral operators;
projection operators into finite dimensional subspaces; spectral the
ory of completely continuous operators; eigenfunction expansions;
Galerkin's method; completely continuous operators in Banach spaces;
the Fredholm alternative
Chapter 13 Approximation Methods for Linear Operator Equations ... 68

Table of Contents Vil
finite basis methods; finite difference methods; separation of vari
ables and eigenfunction expansions for the diffusion equation; rates
of convergence; Galerkin's method in Hubert spaces; collocation
methods; finite difference methods; Fredholm integral equations; the
Nyström method
Chapter 14 Interval Methods for Operator Equations 83
interval arithmetic; interval integration; interval operators; inclusion
isotonicity; nonlinear operator equations with data perturbations
Chapter 15 Contraction Mappings and Iterative Methods 94
fixed point problems; contraction mappings; initial value problems;
two-point boundary value problems
Chapter 16 Fréchet Derivatives 102
Freenet differentiable operators; locally linear operators; the Fréchet
derivative; the Gâteaux derivative; higher Fréchet derivatives; the
Taylor theorem in Banach spaces
Chapter 17 Newton's Method in Banach Spaces 116
Newton's iterative method for nonlinear operator equations; local
convergence; the error squaring property; the Kantorovich theorem;
computational verification of convergence conditions using interval
analysis; interval versions of Newton's method
Chapter 18 Variants of Newton's Method 131
a general theorem; Ostrowski's theorem; Newton's method; the sim
plified Newton method; the SOR-Newton method (generalized New
ton method); a Gauss-Seidel modification
Chapter 19 Homotopy and Continuation Methods 138
homotopies; successive perturbation methods; continuation methods;
curve of zeros; discrete continuation; Davidenko's method; compu
tational aspects
Chapter 20 A Hybrid Method for a Free Boundary Problem 146
Hints for Selected Exercises 160
Further Reading 173
Tndex 177

Preface
The term functional analysis refers to a fruitful and diversified branch of mathe
matics which includes the study of set-theoretic, topological, algebraic, geometric,
order, and analytic properties of mappings in finite and infinite dimensional spaces.
It is characterized by a generality and elegance that is lacking in classical analysis.
Computational mathematics and numerical analysis rely heavily on results from
this theory.
In this book, the main emphasis is on numerical methods for operator equations
— in particular, on the analysis of approximation error in various methods for ob
taining approximate solutions to equations and systems of equations. These might
be algebraic, linear, nonlinear, differential, integral, or other types of equations.
An important part of functional analysis is the extension of techniques for deal
ing with finite dimensional problems to the infinite dimensional case. This allows
us to obtain results which apply at the same time to finite systems of algebraic
equations or equally to differential and integral equations.
In mathematics, there is often a trade-off between generality and precision. As
a result, in any specific application of functional analysis to a particular numerical
problem, there is always the possibility of sharpening results by making use of
special properties of the particular problem. Despite this, the methods of functional
analysis are, at the very least, an excellent starting point for any practical problem.
This text is designed for a one-semester introduction at the first year graduate
level; however, the material can easily be expanded to fill a two-semester course.
It has been taught both ways by the first author at the University of Wisconsin-
Madison and as a one-semester course at the University of Texas at Arlington. By
adding a little additional detail and proceeding at a leisurely pace, Chapters 1-9 and
11-13 can serve as the first semester's material concentrating on linear operator
equations. The remaining material, concentrating on nonlinear operator equations,
can serve as the second semester's material, again with a little additional detail and
proceeding at a comfortable pace. The material as written can be covered in one

X Preface
semester as a concentrated introduction for students who are willing to acquire, in
a short period, the rudiments of a powerful discipline.
An easy way to expand the material to fit a two-semester course is for the in
structor to discuss in detail every one of the more than 100 exercises in the text after
the students have had a try at them. It is no more possible to acquire mathematical
strength and skills by simply sitting in a lecture room and listening to someone talk
about mathematics than it is to acquire physical strength and skills by sitting in a
living room and watching football on television. Therefore, it is essential for the
education of the students that they try all the exercises, which are designed to help
them learn how to discover the mathematics for themselves.
The usual practice of numbering equations along with frequent cross-references
to equations on distant pages has been dropped in this text as an unnecessary en
cumbrance.
Acknowledgements
Computational Functional Analysis was inspired by the earlier works of Louis B.
Rail. We are indebted to Professor Rail for his generous assistance with this second
edition. We would also like to express our appreciation to Edward J. Rothwell of
Michigan State University for examining a late version of the manuscript.

Notation
V universal quantifier (for all, for every) 4
3 existential quantifier (there exists) 4
iff if and only if 6
xry (x,y) belongs to the relation r 5
(x,y) ordered pair, inner product of x and y 5, 20
Nr(xo) r-neighborhoodofxo 109
xy line segment joining x and y 48
||χ|| norm of x 16
d(x,y) distance between x and y 11
A UB union of A and ß 45
A Π B intersection of A and B 45
X x Y Cartesian product of X and Y 5
S Θ T direct sum of 5 and T 25
X Y complement of Y in X 1
AÇB A is a subset of ß 12
AcB A is a proper subset of ß 43
F closure of set Y, right endpoint of interval Y 8, 43
F left endpoint of interval Y 43

xii Notation
I(M) set of all intervals in M 44
M the real numbers 3
Q the rational numbers 13
N the natural numbers (positive integers) 8
E" «-dimensional Euclidean space 4
X linear space; normed linear space; metric space 3
X/Y factor space X modulo Y 6
H Hubert space 22
X* completion of X, dual space of X 14,31
L(H,H) space of bounded linear operators mapping H into H 55
N(L) null space of linear operator L 30
C[a, b] space of continuous functions with max norm 15
h space of square-summable sequences 21
J5?2 [a, b] space of square-integrable functions 22
/ : 5 —
» T function / from 5 into T 8
/~ ' (5) inverse image of S under / 9
fog composition of / and g 9
L linear operator (usually) 50
L* adjoint of bounded linear operator L 54
h/ Riesz représenter of / 30
/ united extension of / 46
P'(xo) Fréchet derivative 103
DP(XQ) Gâteaux derivative 105

1
Introduction
The outcome of any numerical computation will be a finite set of numbers. The
numbers themselves will be finite decimal (or binary) expansions of rational num
bers. Nevertheless, such a set of numbers can represent &function in many ways:
as coefficients of a polynomial; as coefficients of a piecewise polynomial function
(for example a spline function); as Fourier coefficients; as left and right hand end-
points of interval coefficients of an interval valued function; as coefficients of each
of the components of a vector valued function; as values of a function at a finite set
of argument points; etc.
The concepts and techniques of functional analysis we shall study will enable
us to design and apply methods for the approximate solution of operator equations
(differential equations, integral equations, and others). We shall be able to com
pute numerical representations of approximate solutions and numerical estimates
of error. Armed with convergence theorems, we shall know that, by doing enough
computing, we can obtain approximate solutions of any desired accuracy, and know
when we have done so.
Since no previous knowledge of functional analysis is assumed here, a number
of introductory topics will be discussed at the beginning in order to prepare for
discussion of the computational methods.
The literature on functional analysis is now quite extensive, and only a small
part of it is presented here — that which seems most immediately relevant to com
putational purposes. In this introductory study, we hope that the reader will be
brought along far enough to be able to begin reading the more advanced literature
and to apply the techniques to practical problems.
Some knowledge of linear algebra and differential equations will be assumed,

2 Introduction [Ch. 1
and previous study of numerical methods and some experience in computing will
help in understanding the applications to be discussed. No background in measure
theory is assumed; in fact, we will make scant use of those concepts.
In the first part of the study (Chapters 1-10), we introduce a number of different
kinds of topological spaces suitable for investigations of computational methods for
solving linear operator equations. These include Hubert spaces, Banach spaces, and
metric spaces. Linear functionals will play an important role, especially in Hubert
spaces. In fact, these mappings are the source of the namefunctional analysis. We
will see that the Riesz representation theorem plays an important role in computing
when we operate in reproducing kernel Hubert spaces.
The study of order relations in function spaces leads to important computing
methods based on interval valued mappings. In Chapter 17, interval analysis is used
to help construct bounds on the norm of an operator in connection with computa
tionally verifying sufficient conditions for the convergence of an iterative method
for solving a nonlinear operator equation.
In the second part of the study (Chapters 11-13), we turn our attention to meth
ods for the approximate solution of linear operator equations.
In the third part of the study (Chapters 14-20), we investigate methods for the
approximate solution of nonlinear operator equations.
It will be assumed, as the text proceeds, that the reader understands the content
of the exercises to that point. Some hints (and often full solutions) appear from
page 160 onwards; as mentioned in the Preface, however, the reader will learn best
by attempting each exercise before consulting the hints.

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The Project Gutenberg eBook of The Book of the
Homeless (Le livre des sans-foyer)

This ebook is for the use of anyone anywhere in the United
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laws of the country where you are located before using this
eBook.
Title: The Book of the Homeless (Le livre des sans-foyer)
Editor: Edith Wharton
Contributor: Léon Bakst
Maurice Barrès
Sir Max Beerbohm
Sarah Bernhardt
Laurence Binyon
Jacques-Émile Blanche
Edwin Howland Blashfield
Léon Joseph Florentin Bonnat
Paul Bourget
Rupert Brooke
Paul Claudel
Jean Cocteau
Joseph Conrad
Pascal-Adolphe-Jean Dagnan-Bouveret
Eleonora Duse
John Galsworthy
Walter Gay
Jean Léon Gérôme
Charles Dana Gibson
Edmund Gosse
Robert Grant
Thomas Hardy

Paul Hervieu
William Dean Howells
Georges-Louis‫‏‬Humbert‫‏‬
Vincent d' Indy
Henry James
Francis Jammes
Joseph Jacques Césaire Joffre
Maurice Maeterlinck
Edward Sandford Martin
E. René Ménard
Alice Meynell
Claude Monet
Paul Elmer More
Anna de Noailles
Josephine Preston Peabody
Lilla Cabot Perry
Henri de Régnier
Auguste Renoir
Agnes Repplier
Auguste Rodin
Theodore Roosevelt
Edmond Rostand
Théo van Rysselberghe
George Santayana
John Singer Sargent
Igor Stravinsky
André Suarès
Edith Matilda Thomas
Herbert Trench
Emile Verhaeren
Mrs. Humphry Ward
Barrett Wendell
Edith Wharton
Margaret L. Woods
W. B. Yeats

Release date: July 27, 2018 [eBook #57584]
Most recently updated: January 24, 2021
Language: English, French
Credits: Produced by Chuck Greif and the Online Distributed
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*** START OF THE PROJECT GUTENBERG EBOOK THE BOOK OF
THE HOMELESS (LE LIVRE DES SANS-FOYER) ***

Contents.
List of Illustrations
(In certain versions of this etext [in
certain browsers] clicking on the
image will bring up a larger
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(etext transcriber's note)
THE BOOK OF THE HOMELESS

THE BOOK OF THE
HOMELESS
(Le Livre des Sans-Foyer)
EDITED BY
EDITH WHARTON
New York & London
MDCCCCXVI

THE
BOOK OF THE HOMELESS
(LE LIVRE DES SANS-FOYER)
EDITED BY EDITH WHARTON
. .
.
Original Articles in Verse and Prose
Illustrations reproduced from Original Paintings & Drawings
THE BOOK IS SOLD
FOR THE BENEFIT OF THE AMERICAN HOSTELS FOR REFUGEES
(WITH THE FOYER FRANCO-BELGE)
AND OF THE CHILDREN OF FLANDERS RESCUE COMMITTEE
NEW YORK
CHARLES SCRIBNER’S SONS
MDCCCCXVI
COPYRIGHT, 1916, BY CHARLES SCRIBNER’S SONS
D. B. UPDIKE, THE MERRYMOUNT PRESS, BOSTON, U. S. A.

LETTRE DU GÉNÉRAL JOFFRE
République Française
Armées de l’Est
Le Commandant en Chef
Au Grand Quartier Général, le 18 Août, 1915
Les Etats-Unis d’Amérique n’ont pas oublié que la
première page de l’Histoire de leur indépendance a été
écrite avec un peu de sang français.
Par leur inépuisable générosité et leur grande sympathie,
ils apportent aujourd’hui à la France, qui combat pour sa
liberté, l’aide la plus précieuse et le plus puissant réconfort.
J. Joffre

LETTER FROM GENERAL JOFFRE
[TRANSLATION]
Headquarters of the Commander-in-chief
of the Armies of the French Republic
August 18ᵗʰ 1915
The United States of America have never forgotten that
the first page of the history of their independence was partly
written in French blood.
Inexhaustibly generous and profoundly sympathetic, these
same United States now bring aid and solace to France in
the hour of her struggle for liberty.
J. Joffre

INTRODUCTION
It is not only a pleasure but a duty to write the introduction which Mrs.
Wharton requests for “The Book of the Homeless.” At the outset of this war
I said that hideous though the atrocities had been and dreadful though the
suffering, yet we must not believe that these atrocities and this suffering
paralleled the dreadful condition that had obtained in European warfare
during, for example, the seventeenth century. It is lamentable to have to
confess that I was probably in error. The fate that has befallen Belgium is as
terrible as any that befell the countries of Middle Europe during the Thirty
Years’ War and the wars of the following half-century. There is no higher
duty than to care for the refugees and above all the child refugees who have
fled from Belgium. This book is being sold for the benefit of the American
Hostels for Refugees and for the benefit of The Children of Flanders Relief
Committee, founded in Paris by Mrs. Wharton in November, 1914, and
enlarged by her in April, 1915, and chiefly maintained hitherto by American
subscriptions. My daughter, who in November and December last was in
Paris with her husband, Dr. Derby, in connection with the American
Ambulance, has told me much about the harrowing tragedies of the poor
souls who were driven from their country and on the verge of starvation,
without food or shelter, without hope, and with the members of the family
all separated from one another, none knowing where the others were to be
found, and who had drifted into Paris and into other parts of France and
across the Channel to England as a result of Belgium being trampled into
bloody mire. In April last the Belgian Government asked Mrs. Wharton to
take charge of some six hundred and fifty children and a number of helpless
old men and women from the ruined towns and farms of Flanders. This is
the effort which has now turned into The Children of Flanders Rescue
Committee.
I appeal to the American people to picture to themselves the plight of
these poor creatures and to endeavor in practical fashion to secure that they
shall be saved from further avoidable suffering. Nothing that our people can
do will remedy the frightful wrong that has been committed on these
families. Nothing that can now be done by the civilized world, even if the
neutral nations of the civilized world should at last wake up to the

performance of the duty they have so shamefully failed to perform, can
undo the dreadful wrong of which these unhappy children, these old men
and women, have been the victims. All that can be done surely should be
done to ease their suffering. The part that America has played in this great
tragedy is not an exalted part; and there is all the more reason why
Americans should hold up the hands of those of their number who, like
Mrs. Wharton, are endeavoring to some extent to remedy the national
shortcomings. We owe to Mrs. Wharton all the assistance we can give. We
owe this assistance to the good name of America, and above all for the
cause of humanity we owe it to the children, the women and the old men
who have suffered such dreadful wrong for absolutely no fault of theirs.
Theodore Roosevelt

TABLE OF CONTENTS
CONTRIBUTIONS OF WRITERS AND MUSICIANS
PAGE
MAURICE BARRÈS
Les Frères 59
Translation: The Brothers 61
SARAH BERNHARDT
Une Promesse 64
Translation: A Promise 64
LAURENCE BINYON
The Orphans of Flanders. Poem 3
PAUL BOURGET
Après un An 65
Translation: One Year Later 67
RUPERT BROOKE
The Dance. A Song 4
PAUL CLAUDEL
Le Précieux Sang. Poem 5
Translation: The Precious Blood 6
JEAN COCTEAU
La Mort des Jeunes Gens de la Divine Hellade. Fragment. Poem 9
Translation: How the Young Men died in Hellas. A Fragment 11

JOSEPH CONRAD
Poland Revisited 71
VINCENT D’INDY
Musical Score: La légende de Saint Christophe (Acte I, Sc. III) 55
ELEONORA DUSE
Libertà nella Vita 98
Translation: The Right to Liberty 98
JOHN GALSWORTHY
Harvest 99
EDMUND GOSSE
The Arrogance and Servility of Germany 101
ROBERT GRANT
A Message. Poem 14
THOMAS HARDY
Cry of the Homeless. Poem 16
PAUL HERVIEU
Science et Conscience 105
Translation: Science and Conscience 106
WILLIAM DEAN HOWELLS
The Little Children. Poem 17
GÉNÉRAL HUMBERT

Les Arabes avaient Raison 109
Translation: An Heroic Stand 111
HENRY JAMES
The Long Wards 115
FRANCIS JAMMES
Epitaphe. Poem 18
Translation: An Epitaph 19
GÉNÉRAL JOFFRE
Lettre du Général Joffre vii
Translation: Letter from General Joffre viii
MAURICE MAETERLINCK
Notre Héritage 127
Translation: Our Inheritance 127
EDWARD SANDFORD MARTIN
We Who Sit Afar Off 129
ALICE MEYNELL
In Sleep. Poem 20
PAUL ELMER MORE
A Moment of Tragic Purgation 133
COMTESSE DE NOAILLES
Nos Morts. Poem 21
Translation: Our Dead 21

JOSEPHINE PRESTON PEABODY
Two Songs of a Year: 1914-1915
I. Children’s Kisses 23
II. The Sans-Foyer 25
LILLA CABOT PERRY
Rain in Belgium. Poem 26
AGNES REPPLIER
The Russian Bogyman 139
HENRI DE RÉGNIER
L’Exilé. Poem 27
Translation: The Exile 28
THEODORE ROOSEVELT
Introduction ix
EDMOND ROSTAND
Horreur et Beauté. Poem 30
Translation: Horror and Beauty 30
GEORGE SANTAYANA
The Undergraduate Killed in Battle. Poem 32
IGOR STRAVINSKY
Musical Score: Souvenir d’une marche boche 49
ANDRÉ SUARÈS
Chant des Galloises 143

Translation: Song of the Welsh Women 147
EDITH M. THOMAS
The Children and the Flag. Poem 33
HERBERT TRENCH
The Troubler of Telaro. Poem 34
ÉMILE VERHAEREN
Le Printemps de 1915. Poem 37
Translation: The New Spring 38
MRS. HUMPHRY WARD (Mary A. Ward)
Wordsworth’s Valley in War-time 151
BARRETT WENDELL
1915. Poem 40
EDITH WHARTON
Preface xix
The Tryst. Poem 41
MARGARET L. WOODS
Finisterre. Poem 43
W. B. YEATS
A Reason for Keeping Silent. Poem 45
. .
.
The French poems, except M. Rostand’s Sonnet
are translated by Mrs. Wharton

LIST OF ILLUSTRATIONS
CONTRIBUTIONS OF ARTISTS
FOLLOWING
PAGE
LÉON BAKST
Portrait of Jean Cocteau. From an unpublished crayon
sketch 8
Ménade. From a water-colour sketch 126
MAX BEERBOHM
A Gracious Act. (Caricature.) From a water-colour sketch 104
JACQUES-ÉMILE BLANCHE
Portrait of Thomas Hardy. From a photograph of the
painting 16
Portrait of George Moore. From a photograph of the
painting 138
Portrait of Igor Stravinsky. From a study in oils 46
EDWIN HOWLAND BLASHFIELD
A Woman’s Head. From the original drawing 142
LÉON BONNAT
Pegasus. From a pencil and pen-and-ink sketch 70
P. A. J. DAGNAN-BOUVERET
Brittany Woman. From a drawing in coloured crayons 42
WALTER GAY

Interior. From an original water-colour sketch 32
J. L. GÉRÔME
Turkish Soldier. From the original pencil drawing made in
1857 108
CHARLES DANA GIBSON
“The Girl he left behind Him.” From a pen-and-ink sketch 26
ÉMILE-RENÉ MÉNARD
Nude Figure. From a sketch in coloured crayon 150
CLAUDE MONET
Landscape. From an early coloured pastel 22
Boats on a Beach. From an early crayon drawing 100
PIERRE-AUGUSTE RÉNOIR
Portrait of his Son, wounded in the War. From a charcoal
sketch 64
AUGUSTE RODIN
Two Women. From an original water-colour sketch 98
THÉO VAN RYSSELBERGHE
Portrait of André Gide. From a pencil drawing 4
Portrait of Émile Verhaeren. From a pencil drawing 36
Portrait of Vincent d’Indy. From a photograph of the
painting 57
JOHN SINGER SARGENT, R.A.
Portrait of Henry James. From a photograph of the painting 114
Two Heads. From a pencil drawing 132

PREFACE
I
THE HOSTELS
Last year, among the waifs swept to Paris by the great torrent of the flight
from the North, there came to the American Hostels a little acrobat from a
strolling circus. He was not much more than a boy, and he had never before
been separated from his family or from his circus. All his people were
mummers or contortionists, and he himself was a mere mote of the lime-
light, knowing life only in terms of the tent and the platform, the big drum,
the dancing dogs, the tight-rope and the spangles.
In the sad preoccupied Paris of last winter it was not easy to find a
corner for this little figure. But the lad could not be left in the streets, and
after a while he was placed as page in a big hotel. He was given good pay,
and put into a good livery, and told to be a good boy. He tried ... he really
tried ... but the life was too lonely. Nobody knew anything about the only
things he knew, or was particularly interested in the programme of the last
performance the company had given at Liège or Maubeuge. The little
acrobat could not understand. He told his friends at the Hostels how lonely
and puzzled he was, and they tried to help him. But he couldn’t sleep at
night, because he was used to being up till nearly daylight; and one night he
went up to the attic of the hotel, broke open several trunks full of valuables
stored there by rich lodgers, and made off with some of the contents. He
was caught, of course, and the things he had stolen were produced in court.
They were the spangled dresses belonging to a Turkish family, and the
embroidered coats of a lady’s lap-dog....
I have told this poor little story to illustrate a fact which, as time passes,
is beginning to be lost sight of: the fact that we workers among the refugees
are trying, first and foremost, to help a homesick people. We are not
preparing for their new life an army of voluntary colonists; we are seeking
to console for the ruin of their old life a throng of bewildered fugitives. It is
our business not only to feed and clothe and keep alive these people, but to
reassure and guide them. And that has been, for the last year, the task of the
American Hostels for Refugees.

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