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  • 1
    Publication Date: 2005-03-21
    Print ISSN: 0003-6951
    Electronic ISSN: 1077-3118
    Topics: Physics
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  • 2
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    In:  Other Sources
    Publication Date: 2011-08-24
    Description: The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
    Keywords: THEORETICAL MATHEMATICS
    Type: NPO-17121
    Format: text
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  • 3
    Publication Date: 2011-08-24
    Description: The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.
    Keywords: NUMERICAL ANALYSIS
    Type: NPO-16699
    Format: text
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  • 4
    Publication Date: 2011-08-19
    Description: The standard method of multiple shooting for a system of n first-order differential equations with k unknown initial conditions requires the integration of k sets of variational equations on the first shot and n sets of variational equations on every shot thereafter. This paper describes a variant of multiple shooting that requires the solution of k sets of variational equations on every shot. The technique applies to both linear and nonlinear boundary-value problems. Techniques to deal with difficulties unique to the solution of nonlinear problems are suggested.
    Keywords: NUMERICAL ANALYSIS
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  • 5
    Publication Date: 2011-08-16
    Description: Algorithms based on Newton formula for polynomial interpolation and numerical differentiation
    Keywords: MATHEMATICS
    Type: ; UGREVUE(
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  • 6
    Publication Date: 2011-08-19
    Description: Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.
    Keywords: NUMERICAL ANALYSIS
    Type: ACM Transactions on Mathematical Software (ISSN 0098-3500); 10; 45-57
    Format: text
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  • 7
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    Publication Date: 2018-06-08
    Description: This paper summarizes things the author considers important from his past work, and presents some new ideas for use in the implementation of multistep methods. An effort has been made to include material of interest to those of a theoretical bent, as well as to those whose primary interest is in the implementation of methods.
    Type: Numerical Algorithms
    Format: text
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  • 8
    Publication Date: 2019-06-28
    Description: A Gauss-Newton algorithm is presented for solving nonlinear least squares problems. The problem statement may include simple bounds or more general constraints on the unknowns. The algorithm uses a trust region that allows the objective function to increase with logic for retreating to best values. The computations for the linear problem are done using a least squares system solver that allows for simple bounds and linear constraints. The trust region limits are defined by a box around the current point. In its current form the algorithm is effective only for problems with small residuals, linear constraints and dense Jacobian matrices. Results on a set of test problems are encouraging.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-174480 , NAS 1.26:174480 , DE83-016773 , SAND-83-0936-PT-1
    Format: application/pdf
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  • 9
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    Publication Date: 2019-06-28
    Description: Numerical technique has been developed for testing algorithms used to solve differential equations.
    Keywords: MATHEMATICS AND INFORMATION SCIENCES
    Type: NPO-11644 , NASA Tech Briefs (ISSN 0145-319X); 1; 1; P. 136
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  • 10
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    Publication Date: 2018-06-08
    Description: An 8th order explicit Runge-Kutta code, DXRK8, based on formulas of Dorman and Prince has been developed.
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