作为一本科学期刊，ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (TOMS) 记录了数值、符号、代数和几何计算应用的理论基础。它侧重于算法和程序的分析和构建，以及程序和架构的交互。 TOMS 中记录的算法可在 CALGO.ACM.ORG 上作为 ACM 的收集算法获得。

ACM Transactions on Mathematical Software (TOMS) is a scientific journal that focuses on the theoretical foundations of numerical, symbolic, algebraic, and geometric computation applications. It emphasizes the analysis and construction of algorithms and programs, as well as the interaction between programs and architectures. The algorithms recorded in TOMS are available as collected algorithms from ACM at CALGO.ACM.ORG.

《ACM Transactions on Mathematical Software》是一本科学期刊，专注于数值、符号、代数和几何计算应用的理论基础。期刊强调算法和程序的分析与构建，以及程序与架构之间的相互作用。TOMS中记录的算法可在CALGO.ACM.ORG上作为ACM的收集算法获得。

ACM Transactions on Mathematical Software

In its basic form, the reverse mode of computational differentiation yields the gradient of a scalar-valued function at a cost that is a small multiple of the computational work needed to evaluate the function itself. However, the corresponding memory requirement is proportional to the run-time of the evaluation program. Therefore, the practical applicability of the reverse mode in its original formulation is limited despite the availability of ever larger memory systems. This observation leads to the development of checkpointing schedules to reduce the storage requirements. This article presents the function revolve, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion. This routine is intended to be used as an explicit “controller” for running a time-dependent applications program.

Andreas Griewank

Andrea Walther

Algorithm 799: revolve

算法799：旋转

article Free Access Share on Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming Authors: L. S. Lasdon Department of General Business, School of Business Administration, University of Texas, Austin, TX Department of General Business, School of Business Administration, University of Texas, Austin, TXView Profile , A. D. Waren Department of Computer and Information Science, Cleveland State University, Cleveland, OH Department of Computer and Information Science, Cleveland State University, Cleveland, OHView Profile , A. Jain Energy Systems Group, Stanford Research Institute, Menlo Park, CA Energy Systems Group, Stanford Research Institute, Menlo Park, CAView Profile , M. Ratner Department of Systems and Computer Science, Case Western Reserve University, Cleveland, OH Department of Systems and Computer Science, Case Western Reserve University, Cleveland, OHView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 4Issue 1March 1978 pp 34–50https://doi.org/10.1145/355769.355773Published:01 March 1978Publication History 864citation4,441DownloadsMetricsTotal Citations864Total Downloads4,441Last 12 Months466Last 6 weeks62 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

L. S. Lasdon

A. D. Waren

A. Jain

M. Ratner

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

非线性规划的广义简约梯度法代码设计与测试

In this paper we analyze low-cost accurate approximation of the function \(1/x\) using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new -optimal- iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.

Cezary J. Walczyk

Leonid V. Moroz

Volodymyr Samotyy

Jan L. Cieśliński

Optimal approximation of the 1/ <i>x</i> function using Chebyshev polynomials and magic constants

使用切比雪夫多项式和魔数常数对1/<i>x</i>函数的最优逼近

Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: 1) the complete Legendre elliptic integrals of the first and second kinds, 2) the incomplete Legendre elliptic integrals of the first and second kinds, and 3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1–3, arbitrary real Jacobi amplitudes for points 1–2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.

Sean J. Trim

Raymond J. Spiteri

Algorithm xxx: <tt>ellipFor</tt> , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

算法 xxx: <tt>ellipFor</tt>，一个用于广义输入参数的勒让德椭圆积分和雅可比椭圆函数的 Fortran 软件库

We consider solving a sparse linear system using integer (fixed-point) arithmetic. Integer arithmetic has attracted attention in scientific computing because of its high computational efficiency. Furthermore, considering the current circumstances of hardware development, integer arithmetic is expected to become increasingly important. Nevertheless, integer arithmetic has not been widely used for solving linear systems because it lacks robustness against overflow and underflow, making it hard to solve practical problems. Thus, we propose a new integer-based implementation framework for the flexible GMRES (FGMRES) method, which enables integer-based solvers to solve linear systems with the same accuracy as conventional floating-point solvers. In addition, we propose an integer-only algebraic multigrid preconditioner. Combining it with the integer-based FGMRES framework, we develop an integer-based solver. Numerical experiments on CPUs showed that the developed integer-based solver has a comparable convergence rate to floating-point solvers. We also found the test cases where the integer-based solver runs faster than the floating-point solvers.

Kengo Suzuki

Takeshi Fukaya

Takeshi Iwashita

An integer arithmetic-based AMG preconditioned FGMRES solver

基于整数算术的AMG预处理FGMRES求解器

UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying number of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-track smoothers, and combinations. The paper describes the algorithm and its implementation as well as a test suite of examples and tests.

Sivan Toledo

Algorithm XXXX: UltimateKalman, Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

算法XXXX：终极卡尔曼，使用正交变换的灵活卡尔曼滤波与平滑

SPEX Cholesky, SPEX LDL and SPEX Backslash are software packages for exactly solving sparse linear systems, \(A\mathbf{x}=\mathbf{b}\) . SPEX Cholesky, used for symmetric positive definite (SPD) systems, computes an integral Cholesky factorization to solve the system \(A\mathbf{x}=\mathbf{b}\) in time proportional to arithmetic work—to date the only algorithm for SPD linear systems with this property. SPEX LDL extends SPEX Cholesky for symmetric negative definite and symmetric indefinite matrices with exclusively nonzero leading principal minors. SPEX Backslash is a general-purpose exact solver that automatically determines the best ordering and factorization to exactly solve the system \(A\mathbf{x}=\mathbf{b}\) . Computationally, we test the accuracy of MATLAB sparse backslash, the state-of-the-art collection of sparse matrix solvers, revealing it is near perfect for 87% of the tested instances. In addition, we show that SPEX Cholesky outperforms alternate exact solvers in run time; specifically, SPEX Cholesky outperforms the exact solver Linbox and exact LU factorization on 73% and 90% of tested instances, respectively. Each of SPEX Cholesky, SPEX LDL, and SPEX Backslash are implemented in C and are accompanied by easy-to-use Python and MATLAB interfaces. They are distributed via GitHub, as a component of the SPEX software package, and as component of SuiteSparse.

Abbreviation	ACM Trans. Math. Softw.
Journal Impact	2.83
Quartiles(Global)	MATHEMATICS, APPLIED(Q1)

ISSN	0098-3500, 1557-7295
h-index	93

Publication Information	Publisher: Association for Computing Machinery (ACM)，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1975，Proportion of original research papers: 100.00%，Self Citation Rate:3.70%， Gold OA Rate: 2.40%
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：较易

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Algorithm 799: revolve

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

Optimal approximation of the 1/ x function using Chebyshev polynomials and magic constants

Algorithm xxx: `ellipFor` , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

An integer arithmetic-based AMG preconditioned FGMRES solver

Algorithm xxx: `ellipFor` , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

Optimal approximation of the 1/ x function using Chebyshev polynomials and magic constants

An integer arithmetic-based AMG preconditioned FGMRES solver

Algorithm XXXX: UltimateKalman, Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

Algorithm 1XXX: SPEX Cholesky, LDL, and Backslash for Exactly Solving Sparse Linear Systems

ACM Transactions on Mathematical Software

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience

Algorithm 799: revolve

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

Optimal approximation of the 1/ x function using Chebyshev polynomials and magic constants

Algorithm xxx: ellipFor , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

An integer arithmetic-based AMG preconditioned FGMRES solver

Algorithm xxx: ellipFor , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

Optimal approximation of the 1/ x function using Chebyshev polynomials and magic constants

An integer arithmetic-based AMG preconditioned FGMRES solver

Algorithm XXXX: UltimateKalman, Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

Algorithm 1XXX: SPEX Cholesky, LDL, and Backslash for Exactly Solving Sparse Linear Systems

Algorithm xxx: `ellipFor` , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments

Algorithm xxx: `ellipFor` , a Fortran software library for Legendre elliptic integrals and Jacobi elliptic functions with generalized input arguments