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NESC9863 TOEPLITZ.

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

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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.