NESC9863 TOEPLITZ.

TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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1. NAME OR DESIGNATION OF PROGRAM: TOEPLITZ.

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2. COMPUTERS

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Program name	Package id	Status	Status date
TOEPLITZ	NESC9863/01	Tested	20-JUL-1984

Machines used:

Package ID	Orig. computer	Test computer
NESC9863/01	Many Computers	IBM 3081

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3. DESCRIPTION OF PROGRAM OR FUNCTION

TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a
Toeplitz matrix, a circulant matrix, or has one or several block structures based on Toeplitz or circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals.

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4. METHOD OF SOLUTION:

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

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6. TYPICAL RUNNING TIME

NESC9940/01: NEA-DB executed the test case modules included in the package. Execution times on IBM 3081K for the different modules varied from from 0.1 CPU seconds to 3 CPU seconds.

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7. UNUSUAL FEATURES OF THE PROGRAM:

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8. RELATED AND AUXILIARY PROGRAMS

TOEPLITZ is similar in design to LINPACK (NESC0800), following many of the LINPACK conventions. In addition, several TOEPLITZ subroutines call LINPACK routines which are included.

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9. STATUS

Package ID	Status date	Status
NESC9863/01	20-JUL-1984	Tested at NEADB

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10. REFERENCES:

NESC9863/01, included references:

- O.B. Arushanian, M.K. Samarin, V.V. Voevodin, E.E. Tyrtyshnikov,
  B.S. Garbow, J.M. Boyle, W.R. Corwell and K.W. Dritz:
  The TOEPLITZ Package User's Guide.  ANL-83-16  (May 1984)
- B.S. Garbow:
  The TOEPLITZ Package Implementation Guide.  ANL-83-16  (May 1984)

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11. MACHINE REQUIREMENTS

TOEPLITZ is intended for use on many computers; both a single-precision release for long word-length machines (CDC) and a double-precision release for short word-length machines (IBM) are provided.
NESC9940/01: NEA-DB executed the test cases included in the package on IBM 3081K in 232K bytes of main storage.

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12. PROGRAMMING LANGUAGE(S) USED

Package ID	Computer language
NESC9863/01	FORTRAN-IV

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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

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15. NAME AND ESTABLISHMENT OF AUTHORS

                    B. Garbow (Contact)
                    Argonne National Laboratory
                    Mathematics and Computer Science Division
                    9700 South Cass Avenue
                    Argonne, Illinois 60439

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16. MATERIAL AVAILABLE

NESC9863/01

File name	File description	Records
NESC9863_01.003	TOEPLITZ INFORMATION FILE	202
NESC9863_01.004	TOEPLITZ SINGLE-PRECISION SOURCE	1846
NESC9863_01.005	TOEPLITZ DOUBLE-PRECISION SOURCE	1901
NESC9863_01.006	SINGLE-PRECISION DEMONSTRATION PROGRAM	754
NESC9863_01.007	DOUBLE-PRECISION DEMONSTRATION PROGRAM	787
NESC9863_01.008	SINGLE-PRECISION LINPACK ROUTINES	1313
NESC9863_01.009	DOUBLE-PRECISION LINPACK ROUTINES	1360
NESC9863_01.010	JCL FOR TEST CASE EXECUTION	100
NESC9863_01.011	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 1	2
NESC9863_01.012	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 2	2
NESC9863_01.013	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 3	2
NESC9863_01.014	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 4	5
NESC9863_01.015	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 5	5
NESC9863_01.016	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 6	2
NESC9863_01.017	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 7	2
NESC9863_01.018	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 8	2
NESC9863_01.019	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 9	2
NESC9863_01.020	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 10	2
NESC9863_01.021	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 11	2
NESC9863_01.022	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 12	2
NESC9863_01.023	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 13	2
NESC9863_01.024	TOEPLITZ (S.P.) OUTPUT OF TEST CASE 14	2
NESC9863_01.025	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 1	2
NESC9863_01.026	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 2	2
NESC9863_01.027	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 3	2
NESC9863_01.028	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 4	5
NESC9863_01.029	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 5	5
NESC9863_01.030	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 6	2
NESC9863_01.031	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 7	2
NESC9863_01.032	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 8	2
NESC9863_01.033	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 9	2
NESC9863_01.034	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 10	2
NESC9863_01.035	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 11	2
NESC9863_01.036	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 12	2
NESC9863_01.037	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 13	2
NESC9863_01.038	TOEPLITZ (D.P.) OUTPUT OF TEST CASE 14	2

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17. CATEGORIES

P. General Mathematical and Computing System Routines

Keywords: algorithms, matrices, numerical solution.