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ft(T)s 5340 Y 3496 X 0.0 11 11 f.I ft(B)s 3600 X 0.0 11 11 f.S ft(+)s 3689 X(b)s 0.0 11 11 f.I ft(C)s 4060 X(C)s 4171 X 0.0 11 11 f.S ft(\254)s 4308 X(a)s 0.0 11 11 f.I ft(A)s 5296 Y 4457 X 0.0 8 8 f.I ft(H)s 5340 Y 4524 X 0.0 11 11 f.I ft(B)s 4628 X 0.0 11 11 f.S ft(+)s 4717 X(b)s 0.0 11 11 f.I ft(C)s 720 X 5500 Y 2060 X(A)s 2155 X 0.0 11 11 f.R ft(is)s 2257 X 0.0 11 11 f.I ft(m)s 2345 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 0.0 11 11 f.R ft(,)s 2510 X 0.0 11 11 f.I ft(B)s 2605 X 0.0 11 11 f.R ft(is)s 2707 X 0.0 11 11 f.I ft(k)s 2764 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 3045 X(A)s 3140 X 0.0 11 11 f.R ft(is)s 3242 X 0.0 11 11 f.I ft(k)s 3299 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(m)s 0.0 11 11 f.R ft(,)s 3495 X 0.0 11 11 f.I ft(B)s 3590 X 0.0 11 11 f.R ft(is)s 3692 X 0.0 11 11 f.I ft(k)s 3749 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 4060 X(A)s 4155 X 0.0 11 11 f.R ft(is)s 4257 X 0.0 11 11 f.I ft(k)s 4314 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(m)s 0.0 11 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11 f.I ft(C)s 3045 X(C)s 3156 X 0.0 11 11 f.S ft(\254)s 3293 X(a)s 0.0 11 11 f.I ft(A)s 6256 Y 3442 X 0.0 8 8 f.I ft(T)s 6300 Y 3496 X 0.0 11 11 f.I ft(B)s 6256 Y 3576 X 0.0 8 8 f.I ft(H)s 6300 Y 3671 X 0.0 11 11 f.S ft(+)s 3760 X(b)s 0.0 11 11 f.I ft(C)s 4060 X(C)s 4171 X 0.0 11 11 f.S ft(\254)s 4308 X(a)s 0.0 11 11 f.I ft(A)s 6256 Y 4457 X 0.0 8 8 f.I ft(H)s 6300 Y 4524 X 0.0 11 11 f.I ft(B)s 6256 Y 4604 X 0.0 8 8 f.I ft(H)s 6300 Y 4699 X 0.0 11 11 f.S ft(+)s 4788 X(b)s 0.0 11 11 f.I ft(C)s 720 X 6460 Y 2060 X(A)s 2155 X 0.0 11 11 f.R ft(is)s 2257 X 0.0 11 11 f.I ft(m)s 2345 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 0.0 11 11 f.R ft(,)s 2510 X 0.0 11 11 f.I ft(B)s 2605 X 0.0 11 11 f.R ft(is)s 2707 X 0.0 11 11 f.I ft(n)s 2771 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 3045 X(A)s 3140 X 0.0 11 11 f.R ft(is)s 3242 X 0.0 11 11 f.I ft(k)s 3299 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(m)s 0.0 11 11 f.R ft(,)s 3495 X 0.0 11 11 f.I ft(B)s 3590 X 0.0 11 11 f.R ft(is)s 3692 X 0.0 11 11 f.I ft(n)s 3756 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 4060 X(A)s 4155 X 0.0 11 11 f.R ft(is)s 4257 X 0.0 11 11 f.I ft(k)s 4314 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(m)s 0.0 11 11 f.R ft(,)s 4510 X 0.0 11 11 f.I ft(B)s 4605 X 0.0 11 11 f.R ft(is)s 4707 X 0.0 11 11 f.I ft(n)s 4771 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 720 X 6840 Y 804 X 0.0 11 11 f.R ft(\(In)s 959 X(the)s 1121 X(real)s 1312 X(case)s 1527 X(the)s 1689 X(values)s 1997 X(`T')s 2164 X(and)s 2350 X(`C')s 2524 X(have)s 2758 X(the)s 2920 X(same)s 3173 X(meaning.\))s 7920 Y page /Times-Roman /Times-Roman-8 roman-8-mappings AddRoman-8 /f.R /Times-Roman-8 findfont def 0.0 11 11 f.R ft /lineWidthScale 1.0000 def lineWidthScale xsiz mul 1.7 div setlinewidth 720 X 520 Y 2941 X(- 10 -)s 720 X 880 Y 748 X(b\))s 867 X(Matrix-matrix)s 1517 X(products)s 1923 X(where)s 2217 X(one)s 2403 X(matrix)s 2718 X(is)s 2820 X(real)s 3011 X(or)s 3130 X(complex)s 3536 X(symmetric)s 4028 X(or)s 4147 X(complex)s 4553 X(Hermitian:)s 720 X 1200 Y 804 X(_SYMM)s 1224 X(\(SIDE,)s 1560 X(UPLO,)s 1903 X(M,)s 2057 X(N,)s 2192 X(ALPHA,)s 2614 X(A,)s 2749 X(LDA,)s 3030 X(B,)s 3160 X(LDB,)s 3436 X(BETA,)s 3779 X(C,)s 3909 X(LDC\))s 720 X 1360 Y 804 X(_HEMM)s 1229 X(\(SIDE,)s 1565 X(UPLO,)s 1908 X(M,)s 2062 X(N,)s 2197 X(ALPHA,)s 2619 X(A,)s 2754 X(LDA,)s 3035 X(B,)s 3165 X(LDB,)s 3441 X(BETA,)s 3784 X(C,)s 3914 X(LDC\))s 720 X 1680 Y 804 X(Operation)s 1270 X(\()s /Times-Italic /Times-Italic-8 roman-8-mappings AddRoman-8 /f.I /Times-Italic-8 findfont def 0.0 11 11 f.I ft(C)s 1408 X 0.0 11 11 f.R ft(is)s 1510 X(always)s 1842 X 0.0 11 11 f.I ft(m)s 1930 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 0.0 11 11 f.R ft(,)s 2102 X 0.0 11 11 f.I ft(A)s 2197 X 0.0 11 11 f.R ft(is)s 2299 X(symmetric)s 2791 X(for)s 2946 X(the)s 3108 X(_SYMM)s 3528 X(routines,)s 720 X 1840 Y 804 X(and)s 990 X(Hermitian)s 1463 X(for)s 1618 X(the)s 1780 X(_HEMM)s 2205 X(routines\):)s 720 X 2080 Y 2384 X(SIDE)s 2656 X(=`L')s 3258 X(SIDE)s 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X(complex)s 2478 X(symmetric)s 2970 X(or)s 3089 X(complex)s 3495 X(Hermitian)s 3968 X(matrix:)s 720 X 3420 Y 804 X(_SYRK)s 1181 X(\(UPLO,)s 1560 X(TRANS,)s 1977 X(N,)s 2112 X(K,)s 2247 X(ALPHA,)s 2669 X(A,)s 2804 X(LDA,)s 3085 X(BETA,)s 3428 X(C,)s 3558 X(LDC\))s 720 X 3580 Y 804 X(_HERK)s 1186 X(\(UPLO,)s 1565 X(TRANS,)s 1982 X(N,)s 2117 X(K,)s 2252 X(ALPHA,)s 2674 X(A,)s 2809 X(LDA,)s 3090 X(BETA,)s 3433 X(C,)s 3563 X(LDC\))s 720 X 3900 Y 804 X(Operation)s 1270 X(\()s 0.0 11 11 f.I ft(C)s 1408 X 0.0 11 11 f.R ft(is)s 1510 X(always)s 1842 X 0.0 11 11 f.I ft(n)s 1906 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 0.0 11 11 f.R ft(\):)s 720 X 4220 Y 804 X(For)s 985 X(_SYRK)s 1362 X(routines)s 1744 X(\()s 0.0 11 11 f.I ft(C)s 1882 X 0.0 11 11 f.R ft(is)s 1984 X(symmetric\))s 720 X 4460 Y 2204 X(TRANS)s 2593 X(=`N')s 3149 X(TRANS)s 3538 X(=`T')s 720 X 720 X 4780 Y 2120 X 0.0 11 11 f.I ft(C)s 2231 X 0.0 11 11 f.S ft(\254)s 2368 X(a)s 0.0 11 11 f.I ft(AA)s 4736 Y 2584 X 0.0 8 8 f.I ft(T)s 4780 Y 2666 X 0.0 11 11 f.S ft(+)s 2755 X(b)s 0.0 11 11 f.I ft(C)s 3055 X(C)s 3166 X 0.0 11 11 f.S ft(\254)s 3303 X(a)s 0.0 11 11 f.I ft(A)s 4736 Y 3452 X 0.0 8 8 f.I ft(T)s 4780 Y 3506 X 0.0 11 11 f.I ft(A)s 3610 X 0.0 11 11 f.S ft(+)s 3699 X(b)s 0.0 11 11 f.I ft(C)s 720 X 4940 Y 2120 X(A)s 2215 X 0.0 11 11 f.R ft(is)s 2317 X 0.0 11 11 f.I ft(n)s 2381 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 3055 X(A)s 3150 X 0.0 11 11 f.R ft(is)s 3252 X 0.0 11 11 f.I ft(k)s 3309 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 720 X 5320 Y 804 X 0.0 11 11 f.R ft(For)s 985 X(_HERK)s 1367 X(routines)s 1749 X(\()s 0.0 11 11 f.I ft(C)s 1887 X 0.0 11 11 f.R ft(is)s 1989 X(Hermitian\))s 720 X 5560 Y 2197 X(TRANS)s 2586 X(=`N')s 3152 X(TRANS)s 3541 X(=`C')s 720 X 720 X 5880 Y 2107 X 0.0 11 11 f.I ft(C)s 2218 X 0.0 11 11 f.S ft(\254)s 2355 X(a)s 0.0 11 11 f.I ft(AA)s 5836 Y 2571 X 0.0 8 8 f.I ft(H)s 5880 Y 2666 X 0.0 11 11 f.S ft(+)s 2755 X(b)s 0.0 11 11 f.I ft(C)s 3055 X(C)s 3166 X 0.0 11 11 f.S ft(\254)s 3303 X(a)s 0.0 11 11 f.I ft(A)s 5836 Y 3452 X 0.0 8 8 f.I ft(H)s 5880 Y 3519 X 0.0 11 11 f.I ft(A)s 3623 X 0.0 11 11 f.S ft(+)s 3712 X(b)s 0.0 11 11 f.I ft(C)s 720 X 6040 Y 2107 X(A)s 2202 X 0.0 11 11 f.R ft(is)s 2304 X 0.0 11 11 f.I ft(n)s 2368 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(k)s 3055 X(A)s 3150 X 0.0 11 11 f.R ft(is)s 3252 X 0.0 11 11 f.I ft(k)s 3309 X 0.0 11 11 f.S ft(\264)s 0.0 11 11 f.I ft(n)s 720 X 6420 Y 970 X 0.0 11 11 f.R ft(\(In)s 1130 X(the)s 1297 X(real)s 1493 X(case)s 1713 X(the)s 1880 X(values)s 2193 X(`T')s 2365 X(and)s 2556 X(`C')s 2735 X(have)s 2974 X(the)s 3141 X(same)s 3399 X(meaning.)s 3838 X(In)s 3962 X(the)s 4130 X(complex)s 4542 X(case)s 4763 X(TRANS)s 5158 X(=)s 5254 X(`C')s 720 X 6580 Y(is)s 822 X(not)s 991 X(allowed)s 1366 X(in)s 1480 X(_SYRK,)s 1885 X(and)s 2071 X(TRANS)s 2460 X(=)s 2550 X(`T')s 2717 X(is)s 2819 X(not)s 2988 X(allowed)s 3363 X(in)s 3477 X(_HERK.\))s 7920 Y page /Times-Roman /Times-Roman-8 roman-8-mappings AddRoman-8 /f.R 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X(Computer)s 4123 X(with)s 4357 X(Magnetic)s 4809 X(Tape)s 5065 X(Backup)s 720 X 5420 Y(Store,'')s 1080 X 0.0 11 11 f.I ft(University)s 1565 X(of)s 1679 X(Sydney)s 2016 X(Technical)s 2477 X(Report)s 2804 X(No.)s 2989 X(8)s 0.0 11 11 f.R ft(,)s 3100 X(1960.)s 720 X 5740 Y(A.K.)s 965 X(Dave)s 1226 X(and)s 1415 X(I.S.)s 1600 X(Du)s Cff(,)s 1860 X(``Sparse)s 2255 X(Matrix)s 2585 X(Calculations)s 3166 X(on)s 3308 X(the)s 3474 X(CRAY-2,'')s 4003 X 0.0 11 11 f.I ft(Parallel)s 4396 X(Computing)s 0.0 11 11 f.R ft(,)s 4946 X(vol.)s 5147 X(5,)s 5262 X(pp.)s 720 X 5900 Y(55-64,)s 1032 X(July)s 1244 X(1987.)s 720 X 6220 Y(J.)s 823 X(Demmel,)s 1261 X(J.J.)s 1435 X(Dongarra,)s 1907 X(J.)s 2010 X(Du)s 2176 X(Croz,)s 2449 X(A.)s 2588 X(Greenbaum,)s 3159 X(S.)s 3282 X(Hammarling,)s 3898 X(and)s 4089 X(D.)s 4229 X(Sorensen,)s 4692 X(``Prospectus)s 5273 X(for)s 720 X 6380 Y(the)s 906 X(Development)s 1549 X(of)s 1692 X(a)s 1792 X(Linear)s 2129 X(Algebra)s 2532 X(Library)s 2911 X(for)s 3089 X(High-Performance)s 3954 X(Computers,'')s 4588 X(Argonne)s 5022 X(National)s 720 X 6540 Y(Laboratory)s 1234 X(Report,)s 1589 X(ANL-MCS-TM-97,)s 2487 X(September)s 2984 X(1987.)s 720 X 6860 Y(G.)s 889 X(Dietrich,)s 1338 X(``A)s 1551 X(New)s 1819 X(Formulation)s 2426 X(of)s 2580 X(the)s 2777 X(Hypermatrix)s 3400 X(Householder)s 4023 X(QR-decomposition,'')s 5023 X 0.0 11 11 f.I ft(Comput.)s 720 X 7020 Y(Methods)s 1126 X(Appl.)s 1390 X(Mech)s 1660 X(Engrg)s 0.0 11 11 f.R ft(,)s 1991 X(vol.)s 2188 X(9,)s 2299 X(pp.)s 2465 X(273-280,)s 2887 X(1976.)s 720 X 7340 Y(D.)s 860 X(Dodson)s 1235 X(and)s 1426 X(J.)s 1530 X(Lewis,)s 1859 X(``Issues)s 2232 X(relating)s 2600 X(to)s 2719 X(extension)s 3173 X(of)s 3297 X(the)s 3465 X(Basic)s 3743 X(Linear)s 4062 X(Algebra)s 4448 X(Subprograms,'')s 5168 X 0.0 11 11 f.I ft(ACM)s 7920 Y page /Times-Italic /Times-Italic-8 roman-8-mappings AddRoman-8 /f.I /Times-Italic-8 findfont def 0.0 11 11 f.I ft /lineWidthScale 1.0000 def lineWidthScale xsiz mul 1.7 div 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3883 X(1988.)s 720 X 2000 Y(J.J.)s 905 X(Dongarra,)s 1388 X(J.)s 1502 X(DuCroz,)s 1920 X(S.)s 2053 X(Hammarling,)s 2679 X(and)s 2880 X(R.)s 3025 X(Hanson,)s 3432 X(``An)s 3682 X(Extended)s 4140 X(Set)s 4325 X(of)s 4460 X(Fortran)s 4827 X(Basic)s 5115 X(Linear)s 720 X 2160 Y(Algebra)s 1117 X(Subprograms:)s 1779 X(Model)s 2111 X(Implementation)s 2852 X(and)s 3055 X(Test)s 3289 X(Programs,'')s 3855 X 0.0 11 11 f.I ft(ACM)s 4132 X(Trans.)s 4463 X(Math.)s 4767 X(Software)s 0.0 11 11 f.R ft(,)s 5231 X(vol.)s 720 X 2320 Y(14,1,)s 969 X(March)s 1282 X(1988.)s 720 X 2640 Y(J.J.)s 892 X(Dongarra,)s 1362 X(J.)s 1463 X(DuCroz,)s 1868 X(I.S.)s 2052 X(Du)s /Cff { (f) show xsiz pt 20 div neg 0 rmoveto (f) s } bind def Cff(,)s 2311 X(and)s 2499 X(S.)s 2619 X(Hammarling,)s 3232 X(``A)s 3413 X(Set)s 3584 X(of)s 3706 X(Level)s 3986 X(3)s 4072 X(Basic)s 4347 X(Linear)s 4663 X(Algebra)s 5046 X(Subpro-)s 720 X 2800 Y(grams:)s 1062 X(Model)s 1392 X(Implementation)s 2131 X(and)s 2332 X(Test)s 2564 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X(Hammarling,)s 2131 X(and)s 2328 X(D.C.)s 2576 X(Sorensen,)s 3045 X(``Block)s 3419 X(Reduction)s 3910 X(of)s 4041 X(Matrices)s 4464 X(to)s 4590 X(Condensed)s 5118 X(Forms)s 720 X 4400 Y(for)s 875 X(Eigenvalue)s 1396 X(Computations,'')s 2143 X(Argonne)s 2554 X(National)s 2960 X(Laboratory)s 3474 X(MCS-TM-99,)s 4111 X(p.)s 4222 X(91-112,)s 4589 X(September)s 5086 X(1987.)s 720 X 4720 Y(J.J.)s 890 X(Dongarra)s 1330 X(and)s 1516 X(T.)s 1640 X(Hewitt,)s 1996 X(``Implementing)s 2714 X(Dense)s 3016 X(Linear)s 3330 X(Algebra)s 3711 X(Algorithms)s 4242 X(Using)s 4534 X(Multitasking)s 5127 X(on)s 5266 X(the)s 720 X 4880 Y(CRAY)s 1054 X(X-MP-4,'')s 1548 X 0.0 11 11 f.I ft(SIAM)s 1825 X(J.)s 1929 X(Sci)s 2091 X(Stat.)s 2319 X(Comp.)s 0.0 11 11 f.R ft(,)s 2666 X(vol.)s 2863 X(7,)s 2974 X(1,)s 3085 X(pp.)s 3251 X(347-350,)s 3673 X(January,)s 4069 X(1986.)s 720 X 5200 Y(J.J.)s 905 X(Dongarra)s 1360 X(and)s 1561 X(D.C.)s 1813 X(Sorensen,)s 2286 X(``Linear)s 2687 X(Algebra)s 3083 X(on)s 3237 X(High-Performance)s 4095 X(Computers,'')s 4722 X(in)s 4852 X 0.0 11 11 f.I ft(Proceedings)s 720 X 5360 Y(Parallel)s 1109 X(Computing)s 1627 X(85)s 0.0 11 11 f.R ft(,)s 1793 X(ed.)s 1952 X(U.)s 2087 X(Schendel,)s 2545 X(pp.)s 2711 X(113-136,)s 3133 X(North)s 3417 X(Holland.)s 720 X 5680 Y(J.)s 827 X(DuCroz,)s 1238 X(S.)s 1364 X(Nugent,)s 1751 X(J.)s 1858 X(Reid,)s 2130 X(and)s 2324 X(D.)s 2467 X(Taylor,)s 2823 X(``Solving)s 3275 X(Large)s 3565 X(Full)s 3780 X(Sets)s 4000 X(of)s 4127 X(Linear)s 4448 X(Equations)s 4924 X(in)s 5047 X(a)s 5132 X(Paged)s 720 X 5840 Y(Virtual)s 1059 X(Store,'')s 1419 X 0.0 11 11 f.I ft(ACM)s 1679 X(Trans.)s 1993 X(Math.)s 2281 X(Software)s 0.0 11 11 f.R ft(,)s 2729 X(vol.)s 2926 X(7,4,)s 3120 X(pp.)s 3286 X(527-536,)s 3708 X(1981.)s 720 X 6160 Y(I.S.)s 912 X(Du)s Cff(,)s 1180 X(``Full)s 1470 X(Matrix)s 1808 X(Techniques)s 2352 X(in)s 2477 X(Sparse)s 2808 X(Gaussian)s 3249 X(Elimination,'')s 3909 X 0.0 11 11 f.I ft(Numerical)s 4412 X(Analysis)s 4824 X(Proceedings,)s 720 X 6320 Y(Dundee)s 1088 X(1981,)s 1364 X(Lecture)s 1727 X(Notes)s 2006 X(in)s 2120 X(Mathematics)s 2715 X(912)s 0.0 11 11 f.R ft(,)s 2936 X(pp.)s 3102 X(71-84,)s 3414 X(Springer-Verlag,)s 4181 X(1981.)s 720 X 6640 Y(K.)s 857 X(Gallivan,)s 1293 X(W.)s 1454 X(Jalby,)s 1744 X(and)s 1932 X(U.)s 2069 X(Meier,)s 2388 X(``The)s 2660 X(Use)s 2860 X(of)s 2981 X(BLAS3)s 3348 X(in)s 3464 X(Linear)s 3779 X(Algebra)s 4161 X(on)s 4302 X(a)s 4381 X(Parallel)s 4747 X(Processor)s 5204 X(with)s 720 X 6800 Y(a)s 796 X(Heirarchical)s 1363 X(Memory,'')s 1869 X 0.0 11 11 f.I ft(SIAM)s 2146 X(J.)s 2250 X(Sci.)s 2440 X(Stat.)s 2668 X(Comput.)s 0.0 11 11 f.R ft(,)s 3101 X(vol.)s 3298 X(8,)s 3409 X(6,)s 3520 X(pp.)s 3686 X(1079-1084,)s 4218 X(November)s 4708 X(1987.)s 720 X 7120 Y(A.)s 859 X(George)s 1212 X(and)s 1402 X(H.)s 1541 X(Rashwan,)s 2003 X(``Auxiliary)s 2528 X(Storage)s 2896 X(Methods)s 3314 X(for)s 3474 X(Solving)s 3851 X(Finite)s 4142 X(Element)s 4541 X(Systems,'')s 5042 X 0.0 11 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X(P.)s 1486 X(Sguazzero,)s 1997 X(``The)s 2267 X(LU)s 2441 X(Decomposition)s 3141 X(Algorithm)s 3628 X(and)s 3814 X(Its)s 3952 X(E)s /CFi { (f) show xsiz pt 20 div neg 0 rmoveto (\256) s } bind def CFi(cient)s 4352 X(Fortran)s 4704 X(Implementation)s 720 X 2800 Y(on)s 858 X(the)s 1020 X(IBM)s 1256 X(3090)s 1504 X(Vector)s 1829 X(Multiprocessor,'')s 2622 X(IBM)s 2858 X(ECSEC)s 3230 X(Report)s 3557 X(ICE-0006,)s 4046 X(1987.)s 720 X 3120 Y(R.)s 866 X(Schreiber,)s 1357 X(``Module)s 1815 X(Design)s 2170 X(Speci\256cation)s 2788 X(\(Version)s 3215 X(1.0\),'')s 3533 X(SAXPY)s 3938 X(Computer)s 4422 X(Corporation,)s 5025 X(255)s 5235 X(San)s 720 X 3280 Y(Geronimo)s 1193 X(Way,)s 1455 X(Sunnyvale,)s 1975 X(CA)s 2156 X(94086,)s 2487 X(1986.)s 720 X 3600 Y(R.)s 860 X(Schreiber)s 1317 X(and)s 1513 X(B.)s 1653 X(Parlett,)s 2006 X(``Block)s 2379 X(Re\257ectors:)s 2893 X(Theory)s 3247 X(and)s 3444 X(Computation,'')s 4159 X 0.0 11 11 f.I ft(SIAM)s 4447 X(J.)s 4562 X(Numer.)s 4928 X(Anal.)s 0.0 11 11 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X(*)s 2180 X(*)s 2240 X(T)s 2386 X(f)s 2447 X(a)s 2513 X(c)s 2587 X(t)s 2642 X(o)s 2716 X(r)s 2785 X(i)s 2843 X(z)s 2909 X(a)s 2983 X(t)s 3049 X(i)s 3104 X(o)s 3170 X(n)s 3302 X(o)s 3376 X(f)s 3503 X(a)s 3637 X(s)s 3698 X(y)s 3750 X(m)s 3816 X(m)s 3899 X(e)s 3973 X(t)s 4036 X(r)s 4105 X(i)s 4163 X(c)s 4292 X(p)s 4358 X(o)s 4429 X(s)s 4501 X(i)s 4567 X(t)s 4633 X(i)s 4688 X(v)s 4757 X(e)s 4828 X(-)s 4886 X(d)s 4955 X(e)s 5015 X(\256)s 5084 X(n)s 5161 X(i)s 5227 X(t)s 5285 X(e)s 720 X 1480 Y 728 X(*)s 1110 X(m)s 1193 X(a)s 1267 X(t)s 1330 X(r)s 1399 X(i)s 1454 X(x)s 1575 X(A)s 1664 X(.)s 720 X 1590 Y 728 X(*)s 1116 X(B)s 1201 X(l)s 1256 X(o)s 1325 X(c)s 1388 X(k)s 1457 X(e)s 1520 X(d)s 1652 X(v)s 1721 X(e)s 1792 X(r)s 1855 X(s)s 1927 X(i)s 1982 X(o)s 2048 X(n)s 2126 X(,)s 2249 X(c)s 2315 X(a)s 2389 X(l)s 2455 X(l)s 2521 X(i)s 2576 X(n)s 2642 X(g)s 2768 X(L)s 2843 X(e)s 2906 X(v)s 2975 X(e)s 3049 X(l)s 3170 X(3)s 3294 X(B)s 3362 X(LA)s 3497 X(S)s 3578 X(.)s 720 X 1700 Y 728 X(*)s 720 X 1810 Y 1132 X(I)s 1179 X(N)s 1250 X(T)s 1316 X(EG)s 1448 X(E)s 1512 X(R)s 2254 X(I)s 2301 X(N)s 2375 X(F)s 2433 X(O)s 2522 X(,)s 2636 X(LD)s 2763 X(A)s 2852 X(,)s 2961 X(N)s 720 X 1920 Y 1113 X(D)s 1179 X(O)s 1245 X(U)s 1314 X(B)s 1382 X(L)s 1448 X(E)s 1583 X(P)s 1644 X(R)s 1712 X(E)s 1776 X(C)s 1858 X(I)s 1913 X(S)s 1990 X(I)s 2037 X(O)s 2103 X(N)s 2235 X(A)s 2320 X(\()s 2372 X(LD)s 2499 X(A)s 2588 X(,)s 2642 X(*)s 2716 X(\))s 720 X 2030 Y 1132 X(I)s 1179 X(N)s 1250 X(T)s 1316 X(EG)s 1448 X(E)s 1512 X(R)s 2251 X(J)s 2324 X(,)s 2449 X(J)s 2502 X(B)s 720 X 2140 Y 1132 X(I)s 1179 X(N)s 1250 X(T)s 1316 X(EG)s 1448 X(E)s 1512 X(R)s 2235 X(N)s 2304 X(B)s 720 X 2250 Y 1121 X(P)s 1179 X(A)s 1248 X(R)s 1311 X(A)s 1369 X(M)s 1448 X(E)s 1514 X(T)s 1580 X(E)s 1644 X(R)s 2254 X(\()s 2301 X(N)s 2370 X(B)s 2441 X(=)s 2510 X(6)s 2576 X(4)s 2650 X(\))s 720 X 2360 Y 1118 X(EX)s 1250 X(T)s 1316 X(E)s 1380 X(R)s 1443 X(N)s 1509 X(A)s 1580 X(L)s 2235 X(D)s 2301 X(G)s 2372 X(E)s 2425 X(M)s 2491 X(M)s 2588 X(,)s 2697 X(D)s 2768 X(L)s 2834 X(L)s 2900 X(T)s 2984 X(,)s 3093 X(D)s 3167 X(S)s 3225 X(Y)s 3294 X(R)s 3357 X(K)s 3446 X(,)s 3555 X(D)s 3626 X(T)s 3690 X(R)s 3761 X(S)s 3811 X(M)s 720 X 2470 Y 728 X(*)s 720 X 2580 Y 1132 X(I)s 1179 X(N)s 1253 X(F)s 1311 X(O)s 1451 X(=)s 1586 X(0)s 720 X 2690 Y 1113 X(D)s 1179 X(O)s 1322 X(1)s 1388 X(0)s 1525 X(J)s 1649 X(=)s 1784 X(1)s 1862 X(,)s 1971 X(N)s 2060 X(,)s 2169 X(N)s 2238 X(B)s 720 X 2800 Y 1327 X(J)s 1380 X(B)s 1517 X(=)s 1633 X(M)s 1726 X(I)s 1773 X(N)s 1858 X(\()s 1905 X(N)s 1974 X(B)s 2060 X(,)s 2103 X(N)s 2188 X(-)s 2251 X(J)s 2309 X(+)s 2378 X(1)s 2452 X(\))s 720 X 2910 Y 728 X(*)s 720 X 3020 Y 728 X(*)s 1311 X(U)s 1388 X(p)s 1454 X(d)s 1523 X(a)s 1597 X(t)s 1655 X(e)s 1784 X(d)s 1861 X(i)s 1919 X(a)s 1982 X(g)s 2048 X(o)s 2114 X(n)s 2183 X(a)s 2257 X(l)s 2378 X(b)s 2455 X(l)s 2510 X(o)s 2579 X(c)s 2642 X(k)s 2720 X(.)s 720 X 3130 Y 728 X(*)s 720 X 3240 Y 1314 X(C)s 1377 X(A)s 1448 X(L)s 1514 X(L)s 1641 X(D)s 1715 X(S)s 1773 X(Y)s 1842 X(R)s 1905 X(K)s 1990 X(\()s 2056 X(')s 2108 X(L)s 2180 X(o)s 2235 X(w)s 2315 X(e)s 2386 X(r)s 2452 X(')s 2522 X(,)s 2584 X(')s 2631 X(N)s 2708 X(o)s 2851 X(t)s 2914 X(r)s 2975 X(a)s 3038 X(n)s 3109 X(s)s 3170 X(p)s 3236 X(o)s 3307 X(s)s 3371 X(e)s 3442 X(')s 3512 X(,)s 3571 X(J)s 3624 X(B)s 3710 X(,)s 3769 X(J)s 3838 X(-)s 3896 X(1)s 3974 X(,)s 4036 X(-)s 4094 X(1)s 4172 X(.)s 4226 X(0)s 4281 X(D)s 4358 X(0)s 4436 X(,)s 4479 X(A)s 4564 X(\()s 4627 X(J)s 4700 X(,)s 4754 X(1)s 4828 X(\))s 4898 X(,)s 4946 X(LD)s 5073 X(A)s 5162 X(,)s 720 X 3350 Y 1058 X($)s 2048 X(1)s 2126 X(.)s 2180 X(0)s 2235 X(D)s 2312 X(0)s 2390 X(,)s 2433 X(A)s 2518 X(\()s 2581 X(J)s 2654 X(,)s 2713 X(J)s 2782 X(\))s 2852 X(,)s 2900 X(LD)s 3027 X(A)s 3112 X(\))s 720 X 3460 Y 728 X(*)s 720 X 3570 Y 728 X(*)s 1319 X(F)s 1391 X(a)s 1457 X(c)s 1531 X(t)s 1586 X(o)s 1660 X(r)s 1729 X(i)s 1787 X(z)s 1853 X(e)s 1982 X(d)s 2059 X(i)s 2117 X(a)s 2180 X(g)s 2246 X(o)s 2312 X(n)s 2381 X(a)s 2455 X(l)s 2576 X(b)s 2653 X(l)s 2708 X(o)s 2777 X(c)s 2840 X(k)s 2975 X(a)s 3038 X(n)s 3104 X(d)s 3247 X(t)s 3305 X(e)s 3373 X(s)s 3445 X(t)s 3574 X(f)s 3632 X(o)s 3706 X(r)s 720 X 3680 Y 728 X(*)s 1322 X(n)s 1388 X(o)s 1454 X(n)s 1528 X(-)s 1586 X(p)s 1652 X(o)s 1723 X(s)s 1795 X(i)s 1861 X(t)s 1927 X(i)s 1982 X(v)s 2051 X(e)s 2122 X(-)s 2180 X(d)s 2249 X(e)s 2309 X(\256)s 2378 X(n)s 2455 X(i)s 2521 X(t)s 2579 X(e)s 2642 X(n)s 2711 X(e)s 2779 X(s)s 2845 X(s)s 2918 X(.)s 720 X 3790 Y 728 X(*)s 720 X 3900 Y 1314 X(C)s 1377 X(A)s 1448 X(L)s 1514 X(L)s 1641 X(D)s 1712 X(L)s 1778 X(L)s 1844 X(T)s 1924 X(\()s 1987 X(J)s 2040 X(B)s 2126 X(,)s 2169 X(A)s 2254 X(\()s 2317 X(J)s 2390 X(,)s 2449 X(J)s 2518 X(\))s 2588 X(,)s 2636 X(LD)s 2763 X(A)s 2852 X(,)s 2914 X(I)s 2961 X(N)s 3035 X(F)s 3093 X(O)s 3178 X(\))s 720 X 4010 Y 1330 X(I)s 1385 X(F)s 1528 X(\()s 1594 X(I)s 1641 X(N)s 1715 X(F)s 1773 X(O)s 1862 X(.)s 1905 X(N)s 1976 X(E)s 2060 X(.)s 2114 X(0)s 2188 X(\))s 2301 X(G)s 2367 X(O)s 2504 X(TO)s 2708 X(2)s 2774 X(0)s 720 X 4120 Y 728 X(*)s 720 X 4230 Y 1330 X(I)s 1385 X(F)s 1528 X(\()s 1591 X(J)s 1649 X(+)s 1723 X(J)s 1776 X(B)s 1862 X(.)s 1910 X(L)s 1976 X(E)s 2060 X(.)s 2103 X(N)s 2188 X(\))s 2306 X(TH)s 2438 X(EN)s 720 X 4340 Y 728 X(*)s 720 X 4450 Y 728 X(*)s 1509 X(U)s 1586 X(p)s 1652 X(d)s 1721 X(a)s 1795 X(t)s 1853 X(e)s 1987 X(s)s 2048 X(u)s 2114 X(b)s 2180 X(d)s 2257 X(i)s 2315 X(a)s 2378 X(g)s 2444 X(o)s 2510 X(n)s 2579 X(a)s 2653 X(l)s 2774 X(b)s 2851 X(l)s 2906 X(o)s 2975 X(c)s 3038 X(k)s 3116 X(.)s 720 X 4560 Y 728 X(*)s 720 X 4670 Y 1512 X(C)s 1575 X(A)s 1646 X(L)s 1712 X(L)s 1839 X(D)s 1905 X(G)s 1976 X(E)s 2029 X(M)s 2095 X(M)s 2188 X(\()s 2254 X(')s 2301 X(N)s 2378 X(o)s 2521 X(t)s 2584 X(r)s 2645 X(a)s 2708 X(n)s 2779 X(s)s 2840 X(p)s 2906 X(o)s 2977 X(s)s 3041 X(e)s 3112 X(')s 3182 X(,)s 3244 X(')s 3296 X(T)s 3376 X(r)s 3437 X(a)s 3500 X(n)s 3571 X(s)s 3632 X(p)s 3698 X(o)s 3769 X(s)s 3833 X(e)s 3904 X(')s 3974 X(,)s 4017 X(N)s 4102 X(-)s 4165 X(J)s 4234 X(-)s 4297 X(J)s 4350 X(B)s 4421 X(+)s 4490 X(1)s 4568 X(,)s 4627 X(J)s 4680 X(B)s 4766 X(,)s 4825 X(J)s 4894 X(-)s 4952 X(1)s 5030 X(,)s 720 X 4780 Y 1058 X($)s 2254 X(-)s 2312 X(1)s 2390 X(.)s 2444 X(0)s 2499 X(D)s 2576 X(0)s 2654 X(,)s 2697 X(A)s 2782 X(\()s 2845 X(J)s 2903 X(+)s 2977 X(J)s 3030 X(B)s 3116 X(,)s 3170 X(1)s 3244 X(\))s 3314 X(,)s 3362 X(LD)s 3489 X(A)s 3578 X(,)s 3621 X(A)s 3706 X(\()s 3769 X(J)s 3842 X(,)s 3896 X(1)s 3970 X(\))s 4040 X(,)s 4088 X(LD)s 4215 X(A)s 4304 X(,)s 4358 X(1)s 4436 X(.)s 4490 X(0)s 4545 X(D)s 4622 X(0)s 4700 X(,)s 4743 X(A)s 4828 X(\()s 4891 X(J)s 4949 X(+)s 5023 X(J)s 5076 X(B)s 5162 X(,)s 5221 X(J)s 5290 X(\))s 5360 X(,)s 720 X 4890 Y 1058 X($)s 2240 X(LD)s 2367 X(A)s 2452 X(\))s 720 X 5000 Y 728 X(*)s 720 X 5110 Y 728 X(*)s 1512 X(C)s 1586 X(o)s 1638 X(m)s 1718 X(p)s 1784 X(u)s 1861 X(t)s 1919 X(e)s 2053 X(s)s 2114 X(u)s 2180 X(b)s 2246 X(d)s 2323 X(i)s 2381 X(a)s 2444 X(g)s 2510 X(o)s 2576 X(n)s 2645 X(a)s 2719 X(l)s 2840 X(b)s 2917 X(l)s 2972 X(o)s 3041 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X(.)s 720 X 1270 Y 728 X(*)s 1113 X(U)s 1190 X(n)s 1256 X(b)s 1333 X(l)s 1388 X(o)s 1457 X(c)s 1520 X(k)s 1589 X(e)s 1652 X(d)s 1784 X(v)s 1853 X(e)s 1924 X(r)s 1987 X(s)s 2059 X(i)s 2114 X(o)s 2180 X(n)s 2258 X(,)s 2381 X(c)s 2447 X(a)s 2521 X(l)s 2587 X(l)s 2653 X(i)s 2708 X(n)s 2774 X(g)s 2900 X(L)s 2975 X(e)s 3038 X(v)s 3107 X(e)s 3181 X(l)s 3302 X(2)s 3437 X(a)s 3500 X(n)s 3566 X(d)s 3692 X(L)s 3767 X(e)s 3830 X(v)s 3899 X(e)s 3973 X(l)s 4094 X(1)s 4218 X(B)s 4286 X(LA)s 4421 X(S)s 4502 X(.)s 720 X 1380 Y 728 X(*)s 720 X 1490 Y 1132 X(I)s 1179 X(N)s 1250 X(T)s 1316 X(EG)s 1448 X(E)s 1512 X(R)s 2254 X(I)s 2301 X(N)s 2375 X(F)s 2433 X(O)s 2522 X(,)s 2636 X(LD)s 2763 X(A)s 2852 X(,)s 2961 X(N)s 720 X 1600 Y 1113 X(D)s 1179 X(O)s 1245 X(U)s 1314 X(B)s 1382 X(L)s 1448 X(E)s 1583 X(P)s 1644 X(R)s 1712 X(E)s 1776 X(C)s 1858 X(I)s 1913 X(S)s 1990 X(I)s 2037 X(O)s 2103 X(N)s 2235 X(A)s 2320 X(\()s 2372 X(LD)s 2499 X(A)s 2588 X(,)s 2642 X(*)s 2716 X(\))s 720 X 1710 Y 1132 X(I)s 1179 X(N)s 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