1 edition of **An approximation method for solving the sofa problem** found in the catalog.

An approximation method for solving the sofa problem

Kiyoshi Maruyama

- 74 Want to read
- 16 Currently reading

Published
**1971**
by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana
.

Written in English

- Functions,
- Jordan Curves,
- Maxima and minima,
- Polygons

**Edition Notes**

Statement | by Kiyoshi Maruyama |

Series | Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 489, Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 489 |

Classifications | |
---|---|

LC Classifications | QA76 .I4 no. 489, QA482 .I4 no. 489 |

The Physical Object | |

Pagination | iv, 38 p. |

Number of Pages | 38 |

ID Numbers | |

Open Library | OL25453224M |

OCLC/WorldCa | 584626 |

Use Newton’s method with the specified initial approximation x 1 to find x 3, the third approximation to the root of the given equation.(Give your answer to four decimal places.). Lecture 5: Introduction to Approximation Algorithms Many important computational problems are diﬃcult to solve optimally. In fact, many of those problems are NP-hard1, which means that no polynomial-time algorithm exists that solves the problem optimally unless P=NP. A well-known example is the Euclidean traveling.

A new method of solving numerical equations of all orders by continuous approximation, Philosophical Transactions of the Royal Society, vol. (), – CrossRef Google Scholar [8]. since these edges don’t touch, these are k diﬀerent vertices. So the algorithm is a 2-approximation as desired. Here is now another 2-approximation algorithm for Vertex Cover: Algorithm 2: First, solve a fractional version of the problem. Have a variable xi for each vertex with constraint 0 ≤ xi ≤ 1.

Graphical method for solving nonlinear equations Quasi-analytical solutions to polynomial-type equations Numerical solutions to general nonlinear equations.. • devise ﬁnite difference approximations meeting speciﬁca tions on order of accuracy Relevant self-assessment exercises 47 Finite Difference Approximations Recall from Chapters 1 - 4 how the multi-step methods we developed for ODEs are based on a truncated Tay-lor series approximation .

You might also like

Paul Anthony, Christian

Paul Anthony, Christian

Decision support systems

Decision support systems

Frommers Spain & Morocco on £40 a day

Frommers Spain & Morocco on £40 a day

A guide to pleasant places and journeys of historic interest within the county of Waterloo.

A guide to pleasant places and journeys of historic interest within the county of Waterloo.

Turkey and its people [microform]

Turkey and its people [microform]

Study of Export-Import Bank and World Bank.

Study of Export-Import Bank and World Bank.

Silberberg and Schoemans The law of property.

Silberberg and Schoemans The law of property.

Primeval

Primeval

A guide to Australian alcohol data.

A guide to Australian alcohol data.

Business interactions

Business interactions

Coleridges essays & lectures on Shakespeare & some other old poets & dramatists.

Coleridges essays & lectures on Shakespeare & some other old poets & dramatists.

Geology and mineral potential of south-central Newfoundland

Geology and mineral potential of south-central Newfoundland

A procedure for the solution of the two-dimensional sofa problem is described. A new class of polygons, angularly simple polygons, is defined as a class of permissible sofas.

The pattern representation S r (x o) developed for this class of polygons has the advantage of allowing easy polygonal by: 8. DOI: /BF Corpus ID: An approximation method for solving the sofa problem @article{MaruyamaAnAM, title={An approximation method for solving the sofa problem}, author={Kiyoshi Maruyama}, journal={International Journal of Computer & Information Sciences}, year={}, volume={2}, pages={} }.

He also has a nice webpage about moving sofa problems: • Dan Romik, The moving sofa problem. The papers by Maruyama and Gibbs are these: • K. Maruyama, An approximation method for solving the sofa problem, Int.

Comp. Inf. Sci. 2 (), 29– • Philip Gibbs, A computational study of sofas and cars, () Differential Equations and Exact Solutions in the Moving Sofa Problem.

Experimental Mathematics This book has evolved from lectures devoted to applications of the Wentzel - Kramers – Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N −expansion for solving various problem.

Problem solving in physics is not simply a test of understanding the subject, but is an integral part of learning it. In this book, the basic ideas and methods of quantum mechanics are illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step by: 5.

An approximation method for solving the sofa problem. Kiyoshi Maruyama Pages Books; Book Series; Protocols; Reference Works; Proceedings; Other Sites.

; SpringerProtocols; An approximation method for solving the sofa problem. Kiyoshi Maruyama Pages This textbook presents a variety of applied mathematics topics in science and engineering with an emphasis on problem solving techniques using MATLAB. The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book useful for readers without prior MATLAB experi5/5(1).

Maruyama, “An approximation method for solving the sofa problem”, International Journal of Computer and Information Sciences,vol. 2,pp. 29–. The transportation problem in operational research is concerned with finding the minimum cost of transporting a single commodity from a given number of sources (e.g.

factories) to a given number of destinations (e.g. warehouses). These types of problems can be solved by general network methods, but here we use a specific transportation algorithm. Consider solving this problem with input x = −; we ﬁnd a numerical approximation to the exact value z = exp(−) ≈ In solving this problem, we ﬁrst apply Algorithm A, truncating the series after the ﬁrst 25 values.

This yields the formula ˆz = P24 i=0 xi i!. Performing. Approximate Methods for Analysis of Indeterminate Structures (Ref: Chapter 7) Approximate analysis is useful in determining (approximately) the forces and moments in the different members and in coming up with preliminary designs. Based on the preliminary design, a more detailed analysis can be conducted and then the design can be refined.

The sofas in this problem look a bit different than in the standard sofa problem, and currently, the best solution was proposed by Dan Romik, who explains his idea in the above video. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link) http.

Many mathematical problems resist exact solution. Examples include the isomorphism problem and various dynamical order to increase the value of mathematics as an applied discipline, mathematicians have developed various methods for generating approximate solutions to.

To overcome this difficulty, this paper considers an approximation method for the two-stage fuzzy MPMP production planning problem, and turns it to a finite-dimensional optimization problem.

Furthermore, we design a heuristic algorithm, which combines the AM and SA algorithm, to solve the proposed two-stage fuzzy MPMP production planning. Use Newton’s method with initial approximation x 1 = 1 to find x 2, the second approximation to the root of the equation x 4 – x – 1 = 0.

Explain how the method works by first graphing the function and its tangent line at (1, –1). Answer to Use Euler’s method with step size to estimate y(), where y(x) is the solution of the initial-value problem. Use Newton’s method with initial approximation x 1 = –1 to find x 2, the second approximation to the root of the equation x 3 + x + 3 = 0.

Explain how the method works by first graphing the function and its tangent line at (–1, 1). Finite Difference Approximations. Computational Fluid Dynamics. Analysis of a numerical scheme. The Modiﬁed Equation.

Computational Fluid Dynamics. Use the leap-frog method (centered differences) to integrate the diffusion equation. in time. Use the standard centered difference approximation for the second order spatial derivative.!. In physics or engineering education, a Fermi problem, Fermi quiz, Fermi question, Fermi estimate, order-of-magnitude problem, order-of-magnitude estimate, or order estimation is an estimation problem designed to teach dimensional analysis or approximation of extreme scientific calculations, and such a problem is usually a back-of-the-envelope calculation.In this paper, we suggested an successive approximation method and Padé approximants method for the solution of the non-linear differential equation.

First we calculate power series of the given equation system then transform it into Padé (approximants) series form, which give an arbitrary order for solving differential equation numerically.Various numerical methods for the nonlinear Schrödinger equation [3–5] such as finite element methods, finite difference methods, spectral method, etc.

Note that \(F \) is a dimensionless number that lumps the key physical parameter in the problem, \(\dfc \), and the discretization parameters \(\Delta x \) and \(\Delta t \) into a.