A Numerical Library in C for Scientists and Engineers

Front Cover
CRC Press, Nov 23, 1994 - Mathematics - 816 pages
2 Reviews

This extensive library of computer programs-written in C language-allows readers to solve numerical problems in areas of linear algebra, ordinary and partial differential equations, optimization, parameter estimation, and special functions of mathematical physics.

The library is based on NUMAL, the program assemblage developed and used at the Centre for Mathematics and Computer Science in Amsterdam, one of the world's leading research centers. The important characteristic of the library is its modular structure. Because it is highly compact, it is well-suited for use on personal computers.
The library offers the expert a prodigious collection of procedures for implementing numerical methods. The novice can experiment with the worked examples provided and use the more comprehensive procedures to perform mathematical computations. The library provides a powerful research tool for computer scientists, engineers, and applied mathematicians. Applicable materials can be downloaded from the CRC Press website.

 

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Contents

512 Single equation Derivative available
322
513 System of equations No Jacobian matrix
324
B quanewbndl
327
52 Unconstrained optimization
329
523 One variable Derivative available mininder
332
524 More variables Auxiliary procedures
334
B rnklupd
337
D fleupd
338

E tammat
11
G seqvec
12
I symmatvec
13
15 Real matrix vector products
14
C fulsymmatvcc
15
E symresvec
16
B hshcolmat
17
D hshvectam
18
F hshrowtam
19
B elmcol
20
E elmcolvec
21
G elmrowvec
22
J maxelmrow
23
B ichcol
24
D ichrowcol
25
19 Real vector and matrix Rotation
26
110 Real vector and matrix Norms
27
C infnrmcol
28
E onenrmvec
29
F onenrmrow
30
H onenrmmat
31
reascl
32
112 Complex vector and matrix Multiplication
33
113 Complex vector and matrix Scalar products
34
B hshcomcol
35
C hshcomprd
36
114 Complex vector and matrix Elimination
37
B elmcomcol
38
115 Complex vector and matrix Rotation
39
C chsh2
40
116 Complex vector and matrix Norms
41
117 Complex vector and matrix Scaling
42
B sclcom
43
B comsqrt
44
C carpol
45
B comdiv
46
B Ingintsubtract
48
C lngintmult
49
E lngintpower
52
2 Algebraic Evaluations
54
C norderpol
55
D derpol
56
A ortpol
57
C allortpol
58
E sumortpol
59
F sumortpolsym
60
B oddchepolsum
61
C chepol
62
24 Evaluation of Fourier series
63
B cosser
64
C fouser
65
D fouser1
66
E fouser2
67
F comfouser
68
G comfouser1
69
25 Evaluation of continued fractions
71
B chspol
72
C polshtchs
73
E grnnew
74
G lintfmpol
75
27 Operations on orthogonal polynomials
76
3 Linear Algebra
78
B gsselm
79
C onenrminv
82
E gsserb
83
F gssnri
84
312 Calculation of determinant
85
313 Solution of linear equations
86
C solelm
87
D gsssol
88
E gsssolerb
89
314 Matrix inversion
90
B decinv
91
C invl
92
D gssinv
93
315 Iteratively improved solution
94
B gssitisol
96
C itisolerb
98
D gssitisolerb
100
32 Real Symmetric positive definite matrices
101
B chldec1
102
322 Calculation of determinant
103
B chldeterm1
104
B chlsol1
105
C chldecsol2
106
D chldecsol1
107
B chlinv1
108
C chldecinv2
109
D chldecinv1
110
332 Calculation of determinant
115
B decsolsym2
117
B Isqdglinv
119
342 Least squares solution
120
B lsqortdecsol
121
343 Inverse matrix of normal equations Isqinv
122
344 Least squares with linear constraints
123
B Isqrefsol
128
35 Other real matrix problems
131
B solovr
132
352 Solution of underdetermined systems
133
B solund
134
353 Solution of homogeneous equation
135
B homsol
136
354 Pseudoinversion
137
B psdinv
138
36 Real sparse nonsymmetric band matrices
139
362 Calculation of determinant
142
B decsolbnd
143
37 Real sparse nonsymmetric tridiagonal matrices
145
B dectripiv
146
372 Solution of linear equations
148
B decsoltri
149
C soltripiv
150
D decsoltripiv
151
38 Sparse symmetric positive definite band matrices
153
382 Calculation of determinant
155
A chlsolbnd
156
39 Symmetric positive definite tridiagonal matrices
157
392 Solution of linear equations
158
B decsolsymtri
159
310 Sparse real matrices Iterative methods
160
311 Similarity transformation
161
B baklbr
163
3112 Equilibration complex matrices
164
B baklbrcom
166
3113 To Hessenberg form real symmetric
167
B baksymtri2
168
C tfmprevec
169
D tfmsymtri1
170
E baksymtri1
171
3114 To Hessenberg form real asymmetric
172
B bakreahes1
173
C bakreahes2
174
3115 To Hessenberg form complex Hermitian
175
B hshhrmtrival
177
C bakhrmtri
179
3116 To Hessenberg form complex nonHermitian
180
B bakcomhes
182
312 Other transformations
183
B psttfmmat
184
C pretfmmat
185
313 The ordinary eigenvalue problem
186
B vecsymtri
188
C qrivalsymtri
191
D qrisymtri
193
3132 Real symmetric full matrices
195
B eigsym2
196
C eigvalsym1
198
E qrivalsym2
200
F qrisym
201
G qrivalsym1
202
3133 Symmetric matrices Auxiliary procedures
203
B vecperm
204
C rowperm
205
3135 Symmetric matrices Iterative improvement
206
3136 Asymmetric matrices in Hessenberg form
210
B reaveches
212
C reaqri
213
D comvalqri
216
E comveches
218
3137 Real asymmetric full matrices
221
B reaeigl
222
C reaeig3
224
D comeigval
225
E comeigl
227
3138 Complex Hermitian matrices
229
B eighrm
230
C qrivalhrm
232
D qrihrm
233
3139 Complex upperHessenberg matrices
234
B qricomq
236
31310 Complex full matrices
240
B eigcom
241
314 The generalized eigenvalue problem
243
B qzi
247
C hshdecmul
253
D hestgl3
254
E hcstgl2
255
F hsh2col
256
G hsh3col
257
H hsh2row3
259
I hsh2row2
260
J hsh3row3
261
K hsh3row2
263
315 Singular values
264
B qrisngvaldecbid
266
3152 Real full matrices
268
A qrisngval
269
316 Zeros of polynomials
271
B bounds
276
3162 Zeros of orthogonal polynomials
281
B lupzerortpol
282
C selzerortpol
284
D alljaczer
286
E alllagzer
287
3163 Zeros of complex polynomials
288
4 Analytic Evaluations
290
B sumposseries
291
42 Quadrature
297
B integral
299
422 Multidimensional quadrature
303
423 Gaussian quadrature General weights
306
B gsswts
308
C gsswtssym
309
424 Gaussian quadrature Special weights
311
B gsslagwghts
312
43 Numerical differentiation
314
B jacobnmf
315
C jacobnbndf
316
5 Analytic Problems
318
B zeroinrat
320
525 More variables No derivatives
339
526 More variables Gradient available
345
B flemin
351
53 Overdetermined nonlinear systems
354
B gssnewton
358
54 Differential equations Initial value problems
362
B rke
365
C rk4a
367
D rk4na
373
E rk5na
378
F multistep
383
G diffsys
391
H ark
394
I efrk
398
542 First Order Jacobian matrix available
406
B eferk
410
C linigerlvs
417
D Iiniger2
422
E gms
427
F impcx
435
543 First Order Several derivatives available
443
A modifiedtaylor
444
B eft
448
544 Second order No derivatives right hand side
456
B rk2n
459
C rk3
463
D rk3n
465
545 Initial boundary value problem
469
55 Two point boundary value problems
472
B femlag
479
C femlagspher
483
552 Linear methods Second order skew adjoint
488
553 Linear methods Fourth order self adjoint
492
554 Nonlinear methods
500
56 Twodimensional boundary value problems
503
B elimination
506
56 Parameter estimation in differential equations
511
6 Special Functions
529
C arctanh
530
62 Exponential integral
531
B eialpha
533
C enx
534
D nonexpenx
535
622 Sine and cosine integral
537
B sincosfg
538
63 Gamma function
539
B gamma
541
C loggamma
542
D incomgam
543
E incbeta
545
F ibpplusn
546
G ibqplusn
547
H ixqfix
548
I ixpfix
549
64 Error function
550
B nonexperfc
551
C inverseerrorfunction
553
D fresnel
555
E fg
556
65 Bessel functions of integer order
558
A bessjO
559
C bessj
560
D bessyO1
562
E bessy
564
G besspq1
566
652 Bessel functions I and
567
B bessi1
568
D besskO1
569
E bessk
570
F nonexpbessiO
571
G nonexpbessi1
572
H nonexpbessi
573
I nonexpbesskO1
574
J nonexpbessk
576
A bessjaplusn
577
B bessyaO1
578
C bessyaplusn
580
E besszeros
582
F start
585
662 Bessel functions I and K
587
C besskaplusn
589
D nonexpbessiaplusn
590
E nonexpbesskaO1
591
F nonexpbesskaplusn
592
663 Spherical Bessel functions
593
B spherbessy
594
D spherbessk
595
E nonexpspherbessi
596
664 Airy functions
597
B airyzeros
601
7 Interpolation and Approximation
603
B sndremez
604
C minmaxpol
606
Worked Examples
610
rotcomcol
611
comabs
612
carpol
613
lngintadd lngintsubtract lngintmult lngintdivide lngintpower
614
derpol
615
oddchepolsum
616
fouser
617
chspol polchs
618
newgrn grnnew
619
intchs
620
decsol
621
gsssolerb
622
gssinv
623
gssinverb
624
gssitisol
625
chldec2 chlsol2 chlinv2
626
chldecl chlsoll chlinvl
627
chdecsol2 chldeterm2 chldecinv2
628
chldecsol1 chldeterm1 chldecinv1
629
determsym2
631
lsqortdec Isqsol Isqdglinv
632
lsqortdecsol
633
Isqinv
634
lsqdecomp Isqrefsol
635
solovr
636
solund
637
homsol
638
psdinv
640
solbnd decbnd determbnd
641
decsolbnd
642
soltripiv
643
decsoltripiv
644
chldecsolbnd chldetermbnd
645
decsolsymtri
646
eqilbrcom
647
hshhrmtri
648
valsymtri vecsymtri
649
eigsyml
650
comvalqri comveches
652
reaeig3
653
eighrm
654
qrihrm
655
valqricom
656
qricom
657
eigcom
658
qzival
659
qzi
660
qrisngvaldec
662
zerpol bounds
663
allzerortpol
664
seizerortpol
665
alllagzer
666
euler
667
integral
668
tricub
669
gsswtssym
670
gssjacwghts
671
jacobnnf
672
jacobnbndf
673
zeroin
674
zeroinder
675
quanewbnd1
676
minin
677
praxis
678
rnklmin flemin
679
marquardt
680
gssnewton
682
rk4a
685
rk5na
686
multistep
687
diffsys
688
ark
689
efrk
691
efsirk
692
eferk
694
linigerlvs
695
liniger2
696
gms
698
impex
699
modifiedtaylor
701
rk2
704
rk2n
705
rk3
706
rk3n
707
arkmat
708
femlagsym
710
femlag
711
femlagspher
712
femlagskew
713
femhermsym
714
nonlinfemlagskew
715
Function tested richardson
716
elimination
718
peide
720
eialpha
725
sincosint sincosfg
726
recipgamma
727
loggamma
728
ibpplusn
729
inverseerrorfunction
730
fresnel fg
731
bessyOl
732
besspqO besspql
733
besskOl
734
nonexpbessk
735
besspqaOl
736
spherbessi nonexpspherbessi
737
airy
738
newton
739
sndremez
740
References
742
Prototype Declarations
751
Procedure Descriptions
759
Memory Management Utilities
779
Index of Procedures
782
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科学计算导论
希思
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