IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/43614.html
   My bibliography  Save this paper

Constructing a Generator of Matrices with Pattern

Author

Listed:
  • Halkos, George
  • Tsilika, Kyriaki

Abstract

Computations with large matrices work out faster with computer software, even faster creating automatically the matrix of the size and pattern needed. In this paper we propose free computer algebra system Xcas resources to display particular matrices that can be called up directly. Our computer codes provide shortcuts for entering random block diagonal matrices, random triangular matrices, random and specialized band matrices, elementary matrices Eij, Fourier matrices. As for matrices needed in the study of mathematical issues concerning the properties of the roots of a polynomial, we create features with polynomial coefficients. We also propose codes for immediate construction of functional matrices such as Jacobian, bordered Hessian and Wronskian. The computer codes proposed provide visual representation of the matrix pattern (which is traditionally explained using indices and numerals), infinite number of examples using random numbers and immediate construction of large matrices of various forms.

Suggested Citation

  • Halkos, George & Tsilika, Kyriaki, 2012. "Constructing a Generator of Matrices with Pattern," MPRA Paper 43614, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43614
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/43614/1/MPRA_paper_43614.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lloyd, William P & Lee, Cheng F, 1976. "Block Recursive Systems in Asset Pricing Models," Journal of Finance, American Finance Association, vol. 31(4), pages 1101-1113, September.
    2. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
    3. David G. Tarr, 2017. "Distributed Lags, Morishima Matrices, And The Stability Of Economic Models," World Scientific Book Chapters, in: Trade Policies for Development and Transition, chapter 27, pages 627-630, World Scientific Publishing Co. Pte. Ltd..
    4. Arthur F. Veinott, 1969. "Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems," Operations Research, INFORMS, vol. 17(2), pages 262-291, April.
    5. Halkos, George & Tsilika, Kyriaki, 2012. "Stability analysis in economic dynamics: A computational approach," MPRA Paper 41371, University Library of Munich, Germany.
    6. Geoffrey J.D. Hewings, 1985. "Regional Input-Output Analysis," Wholbk, Regional Research Institute, West Virginia University, number 11 edited by Grant I. Thrall, November-.
    7. Batten, D & Martellato, D, 1985. "Classical versus Modern Approaches to Interregional Input-Output Analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 19(3), pages 1-15, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Canning, Patrick & Wang, Zhi, 2004. "A flexible modeling framework to estimate interregional trade patterns and input-output accounts," Policy Research Working Paper Series 3359, The World Bank.
    2. George E. Halkos & Kyriaki D. Tsilika, 2018. "A New Vision of Classical Multi-regional Input–Output Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 571-594, March.
    3. Halkos, George & Tsilika, Kyriaki, 2014. "Perspectives on integrating a computer algebra system into advanced calculus curricula," MPRA Paper 63898, University Library of Munich, Germany.
    4. Myung-jin Jun, 1999. "An Integrated Metropolitan Model Incorporating Demographic-economic, Land-use and Transport Models," Urban Studies, Urban Studies Journal Limited, vol. 36(8), pages 1399-1408, July.
    5. George Halkos & Kyriaki Tsilika, 2015. "A Dynamic Interface for Trade Pattern Formation in Multi-regional Multi-sectoral Input-output Modeling," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 671-681, December.
    6. Halkos, George & Tsilika, Kyriaki, 2016. "Assessing classical input output structures with trade networks: A graph theory approach," MPRA Paper 72511, University Library of Munich, Germany.
    7. Tang, Heiwai & Wang, Fei & Wang, Zhi, 2020. "Domestic segment of global value chains in China under state capitalism✰," Journal of Comparative Economics, Elsevier, vol. 48(4), pages 797-821.
    8. Hughes, David W. & Brown, Cheryl & Miller, Stacy & McConnell, Tom, 2008. "Evaluating the Economic Impact of Farmers’ Markets Using an Opportunity Cost Framework," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 40(1), pages 1-13, April.
    9. Aroca, Patricio & Atienza, Miguel, 2011. "Economic implications of long distance commuting in the Chilean mining industry," Resources Policy, Elsevier, vol. 36(3), pages 196-203, September.
    10. Turner, Karen & Alabi, Oluwafisayo & Smith, Martin & Irvine, John & Dodds, Paul E., 2018. "Framing policy on low emissions vehicles in terms of economic gains: Might the most straightforward gain be delivered by supply chain activity to support refuelling?," Energy Policy, Elsevier, vol. 119(C), pages 528-534.
    11. Randall Jackson & Walter Schwarm & Yasuhide Okuyama & Samia Islam, 2006. "A method for constructing commodity by industry flow matrices," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 40(4), pages 909-920, December.
    12. Pamela Parrish Peterson, 1980. "A Re-Examination Of Seemingly Unrelated Regressions Methodology Applied To Estimation Of Financial Relationships," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 3(3), pages 297-308, September.
    13. George E. Halkos & Kyriaki D. Tsilika, 2016. "Trading Structures for Regional Economies in CAS Software," Computational Economics, Springer;Society for Computational Economics, vol. 48(3), pages 523-533, October.
    14. Sampath Rajagopalan & Medini R. Singh & Thomas E. Morton, 1998. "Capacity Expansion and Replacement in Growing Markets with Uncertain Technological Breakthroughs," Management Science, INFORMS, vol. 44(1), pages 12-30, January.
    15. Allen M. Russell & John A. Rickard & T.D. Howroyd, 1986. "The Effects of Delays on the Stability and Rate of Convergence to Equilibrium of Oligopolies," The Economic Record, The Economic Society of Australia, vol. 62(2), pages 194-198, June.
    16. mercado, p. ruben, 2003. "Empirical economywide modeling in argentina," MPRA Paper 58611, University Library of Munich, Germany.
    17. Thomas C. Sharkey & Joseph Geunes & H. Edwin Romeijn & Zuo‐Jun Max Shen, 2011. "Exact algorithms for integrated facility location and production planning problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 419-436, August.
    18. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.
    19. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    20. Tobias Emonts-Holley & Andrew Ross & J Kim Swales, 2015. "Type II errors in IO multipliers," Working Papers 1504, University of Strathclyde Business School, Department of Economics.

    More about this item

    Keywords

    Matrices with pattern; functional programming; computer software;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:43614. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.