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Национальный исследовательский университет «МЭИ»

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Информационные и сетевые технологии

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варианты расчетных заданий для создания бенчмарка на основе библиотеки IMSL

		номер
	название	страницы
	название	в IMSL
Вариант тема подпрограмм	подпрограмм	eng.

	I. Solution of Linear Systems, Matrix Inversion,
1 and Determinant Evaluation
	High accuracy linear system solution	LSARG	10
	Solve a linear system	LSLRG	11
	Factor and compute condition number	LFCRG	15
2	Factor	LFTRG	18
	Solve after factoring	LFSRG	20
	High accuracy linear system solution after factoring	LFIRG	22
	Compute determinant after factoring	LFDRG	24
	Invert	LINRG	26
3	Complex General Matrices
	High accuracy linear system solution	LSACG	27
	Solve a linear system	LSLCG	30
	Factor and compute condition number	LFCCG	32
4	Factor	LFTCG	35
	Solve a linear system after factoring	LFSCG	37
	High accuracy linear system solution after factoring	LFICG	39
	Compute determinant after factoring	LFDCG	42
	Invert	LINCG	43
5	Real Triangular Matrices
	Solve a linear system	LSLRT	45
	Compute condition number	LFCRT	46
	Compute determinant after factoring	LFDRT	48
	Invert	LINRT	49
6	Complex Triangular Matrices
	Solve a linear system	LSLCT	50
	Compute condition number	LFCCT	52
	Compute determinant after factoring	LFDCT	54
	Invert	LINCT	55
7	Real Positive Definite Matrices
	High accuracy linear system solution	LSADS	56
	Solve a linear system	LSLDS	59
	Factor and compute condition number	LFCDS	61
8	Factor	LFTDS	63
	Solve a linear system after factoring	LFSDS	65
	High accuracy linear system solution after factoring	LFIDS	67
	Compute determinant after factoring	LFDDS	69
	Invert	LINDS	71
9	Real Symmetric Matrices
	High accuracy linear system solution	LSASF	72
	Solve a linear system	LSLSF	75
	Factor and compute condition number	LFCSF	77
10	Factor	LFTSF	80

	Solve a linear system after factoring	LFSSF	81
	High accuracy linear system solution after factoring	LFISF	83
	Compute determinant after factoring	LFDSF	85
11	Complex Hermitian Positive Definite Matrices
	High accuracy linear system solution	LSADH	87
	Solve a linear system	LSLDH	89
	Factor and compute condition number	LFCDH	92
12	Factor	LFTDH	95
	Solve a linear system after factoring	LFSDH	97
	High accuracy linear system solution after factoring	LFIDH	99
	Compute determinant after factoring	LFDDH	101
13	Complex Hermitian Matrices
	High accuracy linear system solution	LSAHF	103
	Solve a linear system	LSLHF	105
	Factor and compute condition number	LFCHF	108
14	Factor	LFTHF	110
	Solve a linear system after factoring	LFSHF	112
	High accuracy linear system solution after factoring	LFIHF	114
	Compute determinant after factoring	LFDHF	117
15	Real Band Matrices in Band Storage
	Solve a tridiagonal system	LSLTR	118
	Solve a tridiagonal system: Cyclic Reduction	LSLCR	119
	High accuracy linear system solution	LSARB	122
16	Solve a linear system	LSLRB	124
	Factor and compute condition number	LFCRB	127
	Factor	LFTRB	130
17	Solve a linear system after factoring	LFSRB	132
	High accuracy linear system solution after factoring	LFIRB	134
	Compute determinant after factoring	LFDRB	136
	Real Band Symmetric Positive Definite Matrices
18	in Band Storage
	High accuracy linear system solution	LSAQS	138
	Solve a linear system	LSLQS	140
	Solve a linear system	LSLPB	143
19	Factor and compute condition number	LFCQS	145
	Factor	LFTQS	148
	Solve a linear system after factoring	LFSQS	149
20	High accuracy linear system solution after factoring	LFIQS	151
	Compute determinant after factoring	LFDQS	153
21	Complex Band Matrices in Band Storage
	Solve a tridiagonal system	LSLTQ	155
	Solve a tridiagonal system: Cyclic Reduction	LSLCQ	156
	High accuracy linear system solution	LSACB	159
22	Solve a linear system	LSLCB	162
	Factor and compute condition number	LFCCB	164
	Factor	LFTCB	167

23	Solve a linear system after factoring	LFSCB	170
	High accuracy linear system solution after factoring	LFICB	172
	Compute determinant after factoring	LFDCB	175
	Complex Band Positive Definite Matrices in Band
24	Storage
	High accuracy linear system solution	LSAQH	176
	Solve a linear system	LSLQH	179
	Solve a linear system	LSLQB	181
25	Factor and compute condition number	LFCQH	184
	Factor	LFTQH	187
	Solve a linear system after factoring	LFSQH	189
26	High accuracy linear system solution after factoring	LFIQH	191
	Compute determinant after factoring	LFDQH	193
27	Real Sparse Linear Equation Solvers
	Factor	LFTXG	199
	Solve a linear system after factoring	LFSXG	204
28	Complex Sparse Linear Equation Solvers
	Factor	LFTZG	212
	Solve a linear system after factoring	LFSZG	217
	Real Sparse Symmetric Positive Definite Linear
29	Equation Solvers
	Symbolic Factor	LSCXD	224
	Compute Factor	LNFXD	228
	Solve a linear system after factoring	LFSXD	232
	Complex Sparse Hermitian Positive Definite Linear
30	Equation Solvers
	Compute Factor	LNFZD	240
	Solve a linear system after factoring	LFSZD	244
31	Real Toeplitz Matrices in Toeplitz Storage
	Solve a linear system	LSLTO	248
	Complex Toeplitz Matrices in Toeplitz Storage
	Solve a linear system	LSLTC	24
32	Complex Circulant Matrices in Circulant Storage
	Solve a linear system	LSLCC	251
	Iterative Methods
	Preconditioned conjugate gradient	PCGRC	253
33	Generalized minimum residual	GMRES	262
	1.2. Linear Least Squares and Matrix
34	Factorization
	1.2.1 Least Squares, QR Decomposition and
	Generalized Inverse
	Solve a Least-squares system	LQRRV	275
35	High accuracy Least squares	LSBRR	279
	Linearly constrained Least squares	LCLSQ	282
36	QR decomposition	LQRRR	286
	Accumulation of QR decomposition	LQERR	289

37	QR decomposition Utilities	LQRSL	292
	QR factor update	LUPQR	295
38	Cholesky Factorization
	Cholesky factoring for rank deficient matrices	LCHRG	299
	Cholesky factor update	LUPCH	301
39	Singular Value Decomposition (SVD)
	Real singular value decomposition	LSVRR	307
	Complex singular value decomposition	LSVCR	311
	Generalized inverse	LSGRR	314
40	II: Eigensystem Analysis
	Real General Problem Ax = λx
	All eigenvalues	EVLRG	325
	All eigenvalues and eigenvectors	EVCRG	327
	Performance index	EPIRG	330
41	Real Symmetric Problem Ax = λx
	All eigenvalues	EVLSF	337
	All eigenvalues and eigenvectors	EVCSF	339
	Extreme eigenvalues	EVASF	341
	Extreme eigenvalues and their eigenvectors	EVESF	343
	Eigenvalues in an interval	EVBSF	345
	Eigenvalues in an interval and their eigenvectors	EVFSF	347
	Performance index	EPISF	350
42	Real General Problem Ax = λ Bx
	All eigenvalues	GVLRG	391
	All eigenvalues and eigenvectors	GVCRG	393
	Performance index	GPIRG	396
43	Real Symmetric Problem Ax = λ Bx
	All eigenvalues	GVLSP	405
	All eigenvalues and eigenvectors	GVCSP	407
	Performance index	GPISP	409
44	Interpolation and Approximation
	Cubic Spline Interpolation
	Easy to use cubic spline routine	CSIEZ	420
	Not-a-knot	CSINT	423
	Derivative end conditions	CSDEC	425
	Hermite	CSHER	429
	Akima	CSAKM	432
	Shape preserving	CSCON	434
	Periodic	CSPER	438
45	Cubic Spline Evaluation and Integration
	Evaluation	CSVAL	440
	Evaluation of the derivative	CSDER	441
	Evaluation on a grid	CS1GD	443
	Integration	CSITG	445

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