SSL II USER'S GUIDE - Lahey Computer Systems

More documents

Recommendations

Info

$SSL2 Extended Capabilities Math Library User's Guide - Lahey ...$

Solution of decomposed system Subroutine name Item Page Remarks LUX CLUX LDLX MDMX BDLX BMDMX BLUX1 Least squares solution A system of linear equations with a real general matrix decomposed into the factors L and U A system of linear equations with a complex general matrix decomposed into the factors L and U A system of linear equations with a positive-definite symmetric matrix decomposed into the factors L, D and L T A system of linear equations with a real indefinite symmetric matrix decomposed into the factors M, D and M T A system of linear equations with a positive-definite symmetric band matrix decomposed into the factors L, D and L T A system of linear equations with a real indefinite symmetric band matrix decomposed into factors M, D, and M T A system of linear equations with a real general band matrix decomposed into the factors L and U Subroutine name Item Page Remarks LAXL Least squares solution with a real matrix (Householder transformation) 390 LAXLR Iterative refinement of the least squares solution with a real matrix 397 LAXLM Least squares minimal norm solution with a real matrix (Singular value decomposition method) GINV Generalized Inverse of a real matrix (Singular value decomposition method) 341 ASVD1 Singular value decomposition of a real matrix (Householder and QR methods) 132 B. Eigenvalues and Eigenvectors Eigenvalues and eigenvectors Subroutine name Item Page Remarks EIG1 Eigenvalues and corresponding eigenvectors of a real matrix (double QR method) 298 CEIG2 Eigenvalues and corresponding eigenvectors of a complex matrix (QR method) 242 SEIG1 SEIG2 HEIG2 BSEG Eigenvalues and corresponding eigenvectors of a real symmetric matrix (QL method) Selected eigenvalues and corresponding eigenvectors of a real symmetric matrix (Bisection method, inverse iteration method) Eigenvalues and corresponding eigenvectors of an Hermition matrix (Householder method, bisection method, and inverse iteration method) Eigenvalues and eigenvectors of a real symmetric band matrix (Rutishauser-Schwarz method, bisection method and inverse iteration method) BSEGJ Eigenvalues and eigenvectors of a real symmetric band matrix (Jennings method) 208 TEIG1 TEIG2 GSEG2 GBSEG Eigenvalues and corresponding eigenvectors of a real symmetric tridiagonal matrix (QL method) Selected eigenvalues and corresponding eigenvectors of a real symmetric tridiagonal matrix (Bisection method, inverse iteration method) Eigenvalues and corresponding eigenvectors of a real symmetric generalized matrix system Ax = λ Bx (Bisection method, inverse iteration method) Eigenvalues and corresponding eigenvectors of a real symmetric band generalized eigenproblem (Jennings method) 454 281 414 462 136 192 186 393 558 560 356 206 583 585 347 335 3
Eigenvalues 4 Subroutine name Item Page Remarks HSQR Eigenvalues of a real Hessenberg matrix (double QR method) 361 CHSQR Eigenvalues of a complex Hessenberg matrix (QR method) 270 TRQL Eigenvalues of a real symmetric tridiagonal matrix (QL method) 598 BSCT1 Selected eigenvalues of a real symmetric tridiagonal matrix (Bisection method) 198 Eigenvectors Subroutine name Item Page Remarks HVEC Eigenvectors of a real Hessenberg matrix (Inverse iteration method) 363 CHVEC Eigenvectors of a complex Hessenberg matrix (Inverse iteration method) 272 BSVEC Eigenvectors of a real symmetric band matrix (Inverse iteration method) 218 Others Subroutine name Item Page Remarks BLNC Balancing of a real matrix 184 CBLNC Balancing of a complex matrix 239 HES1 Reduction of a real matrix to a real Hessenberg matrix (Householder method) 358 CHES2 TRID1 TRIDH BTRID HBK1 CHBK2 TRBK TRBKH Reduction of a complex matrix to a complex Hessenberg matrix (Stabilized elementary transformation) Reduction of a real symmetric matrix to a real symmetric tridiagonal matrix (Householder method) Reduction of an Hermition matrix to a real symmetric tridiagonal matrix (Householder method and diagonal unitary transformation) Reduction of a real symmetric band matrix to a tridiagonal matrix (Rutishauser-Schwarz method) Back transformation and normalization of the eigenvectors of a real Hessenberg matrix Back transformation of the eigenvectors of a complex Hessenberg matrix to the eigenvectors of a complex matrix Back transformation of the eigenvectors of a tridiagonal matrix to the eigenvectors of a real symmetric matrix Back transformation of eigenvectors of a tridiagonal matrix to the eigenvectors of an Hermition matrix NRML Normalization of eigenvectors 498 CNRML Normalization of eigenvectors of a complex matrix 283 GSCHL Reduction of a real symmetric matrix system Ax = λ Bx to a standard form 345 GSBK Back transformation of the eigenvectors of the standard form the eigenvectors of the real symmetric generalized matrix system 268 596 593 221 354 266 589 591 343
Page 1 and 2: SSL II USER’S GUIDE (Scientific S
Page 3 and 4: This document contains technology r
Page 6 and 7: CONTENTS SSL II SUBROUTINE LIST....
Page 8: 11.3 Exponential Integral .........
Page 11: Linear equations 2 Subroutine name
Page 15 and 16: Approximation 6 Subroutine name Ite
Page 17 and 18: Numerical Quadrature 8 Subroutine n
Page 19: J. Pseudo Random Numbers 10 Subrout
Page 22 and 23: (as for the definition of them, see
Page 24: PART I GENERAL DESCRIPTION
Page 27 and 28: GENERAL DESCRIPTION eigenvector cal
Page 29 and 30: GENERAL DESCRIPTION 20 This alphanu
Page 31 and 32: GENERAL DESCRIPTION Matrix definiti
Page 33 and 34: GENERAL DESCRIPTION as shown below,
Page 35 and 36: GENERAL DESCRIPTION ⎡ x1 ⎤ ⎢
Page 37 and 38: CHAPTER 3 LINEAR ALGEBRA 3.1 OUTLIN
Page 39 and 40: GENERAL DESCRIPTION • Determinant
Page 41 and 42: GENERAL DESCRIPTION • Transpositi
Page 43 and 44: GENERAL DESCRIPTION 34 rank (A) = r
Page 45 and 46: GENERAL DESCRIPTION In addition, ob
Page 47 and 48: GENERAL DESCRIPTION 38 routine, how
Page 49 and 50: GENERAL DESCRIPTION 40 implicitly.
Page 51 and 52: GENERAL DESCRIPTION where h is the
Page 53 and 54: GENERAL DESCRIPTION 44 Table 4.7 Su
Page 55 and 56: CHAPTER 5 NONLINEAR EQUATIONS 5.1 O
Page 57 and 58: GENERAL DESCRIPTION 48 Table 5.3 No
Page 59 and 60: GENERAL DESCRIPTION 50 * 1 * T * f
Page 61 and 62: GENERAL DESCRIPTION Comments on use
Page 63 and 64:
GENERAL DESCRIPTION 54 (that is, at
Page 65 and 66:
GENERAL DESCRIPTION 56 is defined a
Page 67 and 68:
GENERAL DESCRIPTION 58 − Calculat
Page 69 and 70:
GENERAL DESCRIPTION 60 y y ( λ,
Page 71 and 72:
GENERAL DESCRIPTION 7.5 SERIES SSL
Page 73 and 74:
GENERAL DESCRIPTION 64 which defini
Page 75 and 76:
GENERAL DESCRIPTION 8.6 LAPLACE TRA
Page 77 and 78:
GENERAL DESCRIPTION Since G(s) is r
Page 79 and 80:
GENERAL DESCRIPTION CHAPTER 9 NUMER
Page 81 and 82:
GENERAL DESCRIPTION Table 9.2 Numer
Page 83 and 84:
GENERAL DESCRIPTION and those combi
Page 85 and 86:
GENERAL DESCRIPTION • Final value
Page 87 and 88:
CHAPTER 11 SPECIAL FUNCTIONS 11.1 O
Page 89 and 90:
GENERAL DESCRIPTION 11.8 BESSEL FUN
Page 91 and 92:
GENERAL DESCRIPTION Table 12.2 Pseu
Page 94 and 95:
A21-11-0101 AGGM, DAGGM Addition of
Page 96 and 97:
value of Zl, l, |Dl| and − if |Dj
Page 98 and 99:
E11-11-0101 AKLAG, DAKLAG Aitken-La
Page 100 and 101:
E11-42-0101 AKMID, DAKMID Two-dimen
Page 102 and 103:
p q p q f 0 1 1 2 () t = 1 − 3t 2
Page 104 and 105:
E12-21-0201 AKMIN, DAKMIN Quasi-Her
Page 106 and 107:
y−1 y0 y1 x−1 x0 x1 x2 x3 Fig.
Page 108 and 109:
C **EXAMPLE** DIMENSION A(100,100),
Page 110 and 111:
This purpose is sometimes obstructe
Page 112 and 113:
By regarding this as a system of li
Page 114 and 115:
Therefore, if the following holds,
Page 116 and 117:
NMIN ≤ Number of evaluations ≤
Page 118 and 119:
holds takes the form. Thus, if the
Page 120 and 121:
example NMAX=2, NMAX is automatical
Page 122 and 123:
Comments on use • Subprograms use
Page 124 and 125:
G24-13-0101 AQMC8, DAQMC8 Multiple
Page 126 and 127:
CALL AQMC8(M,LSUB,FUN,EPSA,EPSR, *N
Page 128 and 129:
I = α + α 1 1∫−1 ∫ 1 1 −1
Page 130 and 131:
G24-13-0201 AQME, DAQME Multiple in
Page 132 and 133:
• Notes The function subprogram a
Page 134 and 135:
• Computing procedure Procedure 1
Page 136 and 137:
NMIN≤Number of evaluations≤NMAX
Page 138 and 139:
much more accurate than required. I
Page 140 and 141:
A21-12-0101 ASSM, DASSM Addition of
Page 142 and 143:
perform singular value decompositio
Page 144 and 145:
The first rotating angle φ 2, that
Page 146 and 147:
500 FORMAT(2I5) 510 FORMAT(4E15.7)
Page 148 and 149:
Table BICD1-1 Condition codes Code
Page 150 and 151:
E12-32-3302 BICD3, DBICD3 B-spline
Page 152 and 153:
E12-31-0102 BIC1, DBIC1 B-spline in
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
E11-32-1101 BIFD1, DBIFD1 B-spline
Page 162 and 163:
WRITE(6,650) IXX,IYY,((R(I,J),I=1,5
Page 164 and 165:
Table BIFD3-1 Condition codes Code
Page 166 and 167:
DO 40 L2=1,M2 ISW=L2-2 WRITE(6,620)
Page 168 and 169:
DO 30 I=1,N1 H=(X(I+1)-X(I))/5.0 XI
Page 170 and 171:
DO 20 J=1,6 V=XI+H*FLOAT(J-1) II=I
Page 172 and 173:
DO 30 I=1,N1 H=(X(I+1)-X(I))/5.0 XI
Page 174 and 175:
The value of In(x) is computed as a
Page 176 and 177:
I11-81-0601 BI0,DBI0 Zero order mod
Page 178 and 179:
I11-81-1001 BJN, DBJN Integer order
Page 180 and 181:
I11-83-0101 BJR, DBJR Real order Be
Page 182 and 183:
I11-81-0201 BJ0,DBJ0 Zero order Bes
Page 184 and 185:
I11-81-0301 BJ1, DBJ1 First order B
Page 186 and 187:
I11-81-1301 BKN, DBKN Integer order
Page 188 and 189:
I v () x ⎧ v ⎪ ⎛ x ⎞ ⎪ 1
Page 190 and 191:
Equation (4.29) can be expressed us
Page 192 and 193:
I11-81-0901 BK1, DBK1 First order m
Page 194 and 195:
=(aij (s) ), balancing is performed
Page 196 and 197:
for the constant vector). However,
Page 198 and 199:
A52-11-0202 BLU1, DBLU1 LU-decompos
Page 200 and 201:
where ⎡1 ⎤ ⎢ ⎥ ⎢ 1 0 ⎥
Page 202 and 203:
• Example Simultaneous linear equ
Page 204 and 205:
where ( x y )( ) s1= n + n + 2m m+
Page 206 and 207:
Replacing the updated knots in the
Page 208 and 209:
For the matrix (T−λ I) shown in
Page 210 and 211:
E32-31-0102 BSC1, DBSC1 B-spline sm
Page 212 and 213:
E32-31-0202 BSC2, DBSC2 B-spline sm
Page 214 and 215:
may assume the minimum. (For detail
Page 216 and 217:
C **EXAMPLE** DIMENSION A(1100),E(1
Page 218 and 219:
attained. If so, it is safe to choo
Page 220 and 221:
Z T Z=P T C T ΛΛΛΛ 2 CP=LL T Wh
Page 222 and 223:
Jennings' acceleration is effective
Page 224 and 225:
obtained by subroutine BSCD2. There
Page 226 and 227:
DO 10 I=1,N 10 W(I)=1.0 CALL BSC1 (
Page 228 and 229:
Given µj as an approximation of λ
Page 230 and 231:
B51-21-0302 BTRID, DBTRID Reduction
Page 232 and 233:
I11-81-1101 BYN, DBYN Integer order
Page 234 and 235:
J ⎛ 1 ⎜− + ⎝ 4 2! Γ 3 −
Page 236 and 237:
a 0 l = 1 l a = i ⎪ 2 2 2 2 2 2 (
Page 238 and 239:
Theoretical precision = 10.66 digit
Page 240 and 241:
Q 1 1 = ∑ k 2 ∑ k= 0 k= 0 2k +
Page 242 and 243:
I11-82-1301 CBJN, DCBJN Integer ord
Page 244 and 245:
is repeatedly applied to k=m,m-1,..
Page 246 and 247:
• For: Single precision: |Im(z)|
Page 248 and 249:
B21-15-0202 CBLNC, DCBLNC Balancing
Page 250 and 251:
I11-82-1401 CBYN, DCBYN Integer ord
Page 252 and 253:
IF(MM.EQ.0) GO TO 50 DO 40 INT=1,MM
Page 254 and 255:
I11-11-0201 CELI2, DCELI2 Complete
Page 256 and 257:
F12-15-0101 CFT, DCFT Multi-variate
Page 258 and 259:
In this routine, the 8 and 2 radix
Page 260 and 261:
where definitions of K1, ..., KM, J
Page 262 and 263:
= n 2 2 = r ⋅ q + q ⋅ r + ( q
Page 264 and 265:
without permutation. So, by the del
Page 266 and 267:
Method This subroutine performs dis
Page 268 and 269:
F12-15-0302 CFTR, DCFTR Discrete co
Page 270 and 271:
NT ( = N1× N2× N3) * One-dimensio
Page 272 and 273:
A11-40-0101 CGSBM, DCGSBM Storage m
Page 274 and 275:
Elements in the general mode Elemen
Page 276 and 277:
DO 30 J=1,N IM=MIN0(J+1,N) DO 30 I=
Page 278 and 279:
Method An n-order complex matrix A
Page 280 and 281:
The process for the complex QR meth
Page 282 and 283:
C **EXAMPLE** COMPLEX ZA(100,100),Z
Page 284 and 285:
C22-15-0101 CJART, DCJART Zeros of
Page 286 and 287:
A22-15-0202 CLU, DCLU LU-decomposit
Page 288 and 289:
A22-15-0602 CLUIV, DCLUIV The inver
Page 290 and 291:
A22-15-0302 CLUX, DCLUX A system of
Page 292 and 293:
B21-15-0702 CNRML, DCNRML Normaliza
Page 294 and 295:
I11-41-0201 COSI, DCOSI Cosine inte
Page 296 and 297:
A11-40-0201 CSBGM, DCSBGM Storage m
Page 298 and 299:
A11-50-0201 CSBSM, DCSBSM Storage m
Page 300 and 301:
A11-50-0101 CSSBM, DCSSBM Storage c
Page 302 and 303:
Method The subroutine uses Muller
Page 304 and 305:
FUNCTION FUN(X) REAL*8 SUM,XP,TERM
Page 306 and 307:
WRITE(6,611) X,P,Q 3 CONTINUE W=W+W
Page 308 and 309:
Therefore if real part uj and imagi
Page 310 and 311:
From matrix F thus obtained and tra
Page 312 and 313:
601 FORMAT(/(5E15.5)) 610 FORMAT('0
Page 314 and 315:
Theoretical precision = 10.04 digit
Page 316 and 317:
trigonometric function values neces
Page 318 and 319:
in the sense that it can be utilize
Page 320 and 321:
Step 4: Discrete cosine transform (
Page 322 and 323:
the maximum value of (power of 2) +
Page 324 and 325:
Method This subroutine applies disc
Page 326 and 327:
It also calculates norm f based on
Page 328 and 329:
• Example By inputting n sample p
Page 330 and 331:
F11-11-0101 FCOST, DFCOST Discrete
Page 332 and 333:
The equations shown in (4.3) can be
Page 334 and 335:
The degree of error decerement grea
Page 336 and 337:
Method This subroutine applies disc
Page 338 and 339:
terms is about nlog2 n. To save sto
Page 340 and 341:
Even when the dimension differs, th
Page 342 and 343:
F11-21-0101, FSINT, DFSINT Discrete
Page 344 and 345:
B52-11-0101 GBSEG, DGBSEG Eigenvalu
Page 346 and 347:
For detailed information about the
Page 348 and 349:
E51-30-0301 GCHEB, DGCHEB Different
Page 350 and 351:
A25-31-0101 GINV, DGINV Moore-Penro
Page 352 and 353:
B22-10-0402 GSBK, DGSBK Back transf
Page 354 and 355:
B22-21-0302 GSCHL, DGSCHL Reduction
Page 356 and 357:
B22-21-0201 GSEG2, DGSEG2 Eigenvalu
Page 358 and 359:
The above processing are accomplish
Page 360 and 361:
Comments • Subprogram used SSL II
Page 362 and 363:
In this case, the current stepsize
Page 364 and 365:
For further information, refer to t
Page 366 and 367:
WRITE(6,630) (J,J=INT,LST) WRITE(6,
Page 368 and 369:
Method An n-order real matrix A is
Page 370 and 371:
B21-11-0402 HSQR,DHSOR Eigenvalues
Page 372 and 373:
B21-11-0502 HVEC,DHVEC Eigenvectors
Page 374 and 375:
CALL HVEC(A,100,N,ER,EI,IND,M,EV,10
Page 376 and 377:
E51-30-0401 ICHEB, DICHEB Indefinit
Page 378 and 379:
I11-71-0301 IERF, DIERF Inverse err
Page 380 and 381:
(c) 2.5 10 -3 ≤x
Page 382 and 383:
I11-61-0201 IGAM2, DIGAM2 Incomplet
Page 384 and 385:
I11-91-0301 INDF, DINDF Inverse nor
Page 386 and 387:
E12-21-0101 INSPL, DINSPL Cubic spl
Page 388 and 389:
F20-01-0101 LAPS1, DLAPS1 Inversion
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
In each of the above, the delay fac
Page 396 and 397:
This subroutine calculates f(t) for
Page 398 and 399:
10 READ(5,510) (B(I),I=1,N) WRITE(6
Page 400 and 401:
610 FORMAT(///10X,'CONSTANT VECTOR=
Page 402 and 403:
A25-21-0101 LAXLM, DLAXLM Least squ
Page 404 and 405:
Where ~ b is an n-dimensional vecto
Page 406 and 407:
A25-11-0401 LAXLR, DLAXLR Iterative
Page 408 and 409:
A22-11-0401 LAXR, DLAXR Iterative r
Page 410 and 411:
esults, this indicates that the con
Page 412 and 413:
• Example In this example, l syst
Page 414 and 415:
Table LBX1R-1 Condition codes code
Page 416 and 417:
A22-15-0101 LCX,DLCX A system of li
Page 418 and 419:
A22-15-0401 LCXR,DLCXR Iterative re
Page 420 and 421:
x (1) is e (1) (=x (1) − x), its
Page 422 and 423:
Method Given the LDL T decomposed m
Page 424 and 425:
Method To solve a system of linear
Page 426 and 427:
500 FORMAT(I5) 510 FORMAT(2F10.0) 6
Page 428 and 429:
C **EXAMPLE** EXTERNAL FUN A=-5.0 B
Page 430 and 431:
e resumed by calling this subroutin
Page 432 and 433:
C21-41-0101 LOWP, DLOWP Zeros of a
Page 434 and 435:
D21-10-0101 LPRS1, DLPRS1 Linear pr
Page 436 and 437:
(which is derived form other constr
Page 438 and 439:
• Basic inveerse matrix B -1 for
Page 440 and 441:
A52-21-0101 LSBIX, DLSBIX A system
Page 442 and 443:
A52-31-0101 LSBX, DLSBX A system of
Page 444 and 445:
A52-31-0401 LSBXR, DLSBXR Iterative
Page 446 and 447:
• Accuracy estimation for approxi
Page 448 and 449:
C **EXAMPLE** DIMENSION A(5050),B(1
Page 450 and 451:
• Example An approximate solution
Page 452 and 453:
This subroutine make use of the cha
Page 454 and 455:
A22-51-0101 LSX, DLSX A system of l
Page 456 and 457:
A22-51-0401 LSXR, DLSXR Iterative r
Page 458 and 459:
A52-11-0501 LTX, DLTX A system of l
Page 460 and 461:
( ) m k+ 1 ,k ( k ) ( k = a ) k+ 1,
Page 462 and 463:
Method This subroutine computes the
Page 464 and 465:
500 FORMAT(I5) 510 FORMAT(4E15.7) 6
Page 466 and 467:
y n i =∑ j= 1 a ij x j , i = 1,..
Page 468 and 469:
The subroutines PBM and PGM are use
Page 470 and 471:
SUBROUTINE PCM(ICOM,L,ZA,K,M,N) DIM
Page 472 and 473:
The subroutines PSM and PGM in this
Page 474 and 475:
A21-11-0401 MGSM, DMGSM Multiplicat
Page 476 and 477:
for the iteration vector xk and if
Page 478 and 479:
• If 2α k < α min < 4α k , the
Page 480 and 481:
Giving MAX: For a variable vector x
Page 482 and 483:
ϕ (α) f 0 f 1 f 2 α k 2α k 4α
Page 484 and 485:
Method The multiplication ( y ) is
Page 486 and 487:
A21-12-0301 MSSM, DMSSM Multiplicat
Page 488 and 489:
Method This subroutine performs mul
Page 490 and 491:
I11-91-0201 NDFC, DNDFC Complementa
Page 492 and 493:
Table NLPG1-1 Condition codes Code
Page 494 and 495:
( x , λλλλ ) ∇ φ( x λλλλ
Page 496 and 497:
C24-11-0101 NOLBR, DNOLBR Solution
Page 498 and 499:
k T ( y) ≈ f ( y ) + g ( y − )
Page 500 and 501:
value for an additional evaluation
Page 502 and 503:
2) To compute the difference approx
Page 504 and 505:
MAX The function evaluation count i
Page 506 and 507:
m n 2 ∑∑( fi / x j ) / ( mn) v
Page 508 and 509:
500 FORMAT(I5) 510 FORMAT(5E15.7) 6
Page 510 and 511:
EPSA ..... Input. Absolute error to
Page 512 and 513:
IF(ICON.EQ.30000) STOP GO TO 10 20
Page 514 and 515:
c ( x − xm )( x − x−1 ) ... (
Page 516 and 517:
− k > 2 and max (ERKM1, ERKM2)
Page 518 and 519:
H11-20-0151 ODGE, DODGE A stiff sys
Page 520 and 521:
Table ODGE-1 Condition codes Code M
Page 522 and 523:
Method Both Gear’s and Adams meth
Page 524 and 525:
xm+1 is determined, solution ye at
Page 526 and 527:
8) Corrector iteration This subrout
Page 528 and 529:
Table ODRK1-1 Condition codes Code
Page 530 and 531:
h′ = + { 6 min hi hi fi ( x0, y0
Page 532 and 533:
Thus, this subroutine is used with
Page 534 and 535:
J12-20-0101 RANB2 Generation of bin
Page 536 and 537:
J11-30-0101 RANE2 Generation of exp
Page 538 and 539:
2) For u − 0 . 5 > 0. 46875 G -1
Page 540 and 541:
J12-10-0101 RANP2 Generation of Poi
Page 542 and 543:
J11-10-0101 RANU2 Generation of uni
Page 544 and 545:
There is a theory that such a perio
Page 546 and 547:
is coupled such as Pi (IXi, IXi+1)
Page 548 and 549:
m = m1 + m2 + ... + ms One call of
Page 550 and 551:
One call of this subroutine enables
Page 552 and 553:
F11-31-0101 RFT, DRFT Discrete real
Page 554 and 555:
from α α α x1 k x2 k x1 0 1 =
Page 556 and 557:
faster than second order. • K pol
Page 558 and 559:
Letting ( ) λ 2 ( ) σ ( x) = x +
Page 560 and 561:
C **EXAMPLE** DIMENSION Y(3,10),F(3
Page 562 and 563:
A52-31-0202 SBDL, DSBDL LDL T -deco
Page 564 and 565:
A52-21-0202 SBMDM, DSBMDM MDM T dec
Page 566 and 567:
1) Determines 2) If ( k − 1) ( k
Page 568 and 569:
DO 10 I=1,N WRITE(6,630) I,(EV(I,J)
Page 570 and 571:
eigenvectors are determined using t
Page 572 and 573:
A21-11-0201 SGGM, DSGGM Subtraction
Page 574 and 575:
G23-11-0101 SIMP2, DSIMP2 Integrati
Page 576 and 577:
a ( 4, 2 ) ( 2, 1 ) ( 5, 2 ) ( 1, 0
Page 578 and 579:
I11-41-0101 SINI, DSINI Sine integr
Page 580 and 581:
C **EXAMPLE** DIMENSION A(5050) 10
Page 582 and 583:
i.e., -s is stored in IP (k+1). The
Page 584 and 585:
E31-11-0101 SMLE1, DSMLE1 Data smoo
Page 586 and 587:
E31-21-0101 SMLE2, DSMLE2 Data smoo
Page 588 and 589:
E11-21-0101 SPLV, DSPLV Cubic splin
Page 590 and 591:
(c) (ISW(1) =3,DY (1)=, f"( x1)/f"(
Page 592 and 593:
B21-21-0602 TEIG1, DTEIG1 Eigenvalu
Page 594 and 595:
B21-21-0702 TEIG2, DTEIG2 Selected
Page 596 and 597:
• Direct sum of submatrices If T
Page 598 and 599:
B21-21-0802 TRBK, DTRBK Back transf
Page 600 and 601:
B21-25-0402 TRBKH, DTRBKH Back tran
Page 602 and 603:
B21-25-0302 TRIDH, DTRIDH Reduction
Page 604 and 605:
where, l = n − k + 1 1 2 1 = k tl
Page 606 and 607:
( ( ) ) ( ( ) ) ( ( ) ) 2 σ k k 2
Page 608 and 609:
T= d 1 e 1 e 1 d 2 e 2 0 e 2 e n−
Page 610 and 611:
C23-11-0111 TSDM, DTSDM Zero of a r
Page 612 and 613:
• Convergence criteria The follow
Page 614 and 615:
Variables a, b, and c have the foll
Page 616 and 617:
APPENDIX A AUXILIARY SUBROUTINES A.
Page 618 and 619:
A.3 MGSSL Printing of condition mes
Page 620 and 621:
A.5 ASUM(BSUM), DSUM(DBSUM) Product
Page 622 and 623:
A.7 IRADIX Radix of the floating-po
Page 624 and 625:
APPENDIX B ALPHABETIC GUIDE FOR SUB
Page 626 and 627:
TableB.1-conteimued Subroutine Clas
Page 628 and 629:
B.3 AUXILIARY SUBROUTINES Table B.3
Page 630 and 631:
Interpolation and approximation Cod
Page 632 and 633:
[20] Brezinski, C. Acceleration de
Page 634 and 635:
[82] Uno,T. Bessel Function. Baifuk
Page 636 and 637:
Author Subroutine Item T. Torii ECH
show all

SSL II USER'S GUIDE - Lahey Computer Systems

Create successful ePaper yourself

Delete template?

Save as template?