Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB

Authors: Tobin A. Driscoll

Source: ACM Transactions on Mathematical Software. 31:239-251

Subject Terms: Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.), Schwarz-Christoffel-type mappings, General theory of numerical methods in complex analysis (potential theory, etc.), Software, source code, etc. for problems pertaining to functions of a complex variable, Packaged methods for numerical algorithms, 0101 mathematics, 16. Peace & justice, 01 natural sciences

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/toms/toms31.html#Driscoll05
https://dl.acm.org/doi/10.1145/1067967.1067971
https://dl.acm.org/citation.cfm?doid=1067967.1067971
https://doi.org/10.1145/1067967.1067971

Recovering Holomorphic Functions from Their Real or Imaginary Parts without the Cauchy--Riemann Equations: Recovering holomorphic functions from their real or imaginary parts without the Cauchy--Riemann equations

Authors: Shaw, W.T.

Source: SIAM Review. 46:717-728

Subject Terms: Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable, 0103 physical sciences, Software, source code, etc. for problems pertaining to functions of a complex variable, Cauchy--Riemann equations, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 0101 mathematics, computer algebra, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, 01 natural sciences, complex analysis

File Description: application/xml

Access URL: https://epubs.siam.org/doi/pdf/10.1137/S0036144503432151
https://www.jstor.org/stable/20453575
https://ui.adsabs.harvard.edu/abs/2004SIAMR..46..717S/abstract
https://dblp.uni-trier.de/db/journals/siamrev/siamrev46.html#Shaw04
https://epubs.siam.org/doi/10.1137/S0036144503432151
https://ora.ox.ac.uk/objects/uuid:8b79f92b-73db-4a55-82f1-2c6eed22a1f6

Improved validated bounds for Taylor coefficients and for Taylor remainder series

Authors: Neher, Markus

Source: Journal of Computational and Applied Mathematics. 152:393-404

Subject Terms: 0102 computer and information sciences, 01 natural sciences, General theory of numerical methods in complex analysis (potential theory, etc.), Algorithms with automatic result verification, 0101 mathematics, ddc:510, numerical examples, Bounds for Taylor coefficients of analytic functions, Applied Mathematics, Interval and finite arithmetic, enclosure methods, Software, source code, etc. for problems pertaining to functions of a complex variable, Complex interval arithmetic, Mathematical software, arithmetic, Power series (including lacunary series) in one complex variable, mathematical software, Computational Mathematics, Computation of special functions and constants, construction of tables, complex interval, bounds for Taylor coefficients of analytic functions, Packaged methods for numerical algorithms, Enclosure methods, Mathematics

File Description: application/xml

Access URL: https://zbmath.org/1912281
https://doi.org/10.1016/s0377-0427(02)00719-7
https://www.sciencedirect.com/science/article/pii/S0377042702007197
https://ui.adsabs.harvard.edu/abs/2003JCoAM.152..393N/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042702007197
http://na.math.kit.edu/neher/preprnts/neher_2003_improved_taylor_JCAM152.pdf

UNIQUENESS POLYNOMIALS FOR ENTIRE FUNCTIONS: Uniqueness polynomials for entire functions.

Authors: Julie Tzu-Yueh Wang, William Cherry

Source: International Journal of Mathematics. 13:323-332

Subject Terms: Software, source code, etc. for problems pertaining to functions of a complex variable, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 0101 mathematics, 01 natural sciences, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

File Description: application/xml

Access URL: https://zbmath.org/1911936
https://doi.org/10.1142/s0129167x02001344
https://www.worldscientific.com/doi/abs/10.1142/S0129167X02001344

Computing the zeros of quaternion polynomials: Computing the zeros of quaternion polynomials.

Authors: Serôdio, R., Pereira, E., Vitória, J.

Source: Computers & Mathematics with Applications. 42:1229-1237

Subject Terms: Computational Mathematics, Computational Theory and Mathematics, Functions of hypercomplex variables and generalized variables, Modelling and Simulation, Software, source code, etc. for problems pertaining to functions of a complex variable, Quaternionic polynomials, Numerical computation of solutions to single equations, Right (and left) quaternionic eigenvalues, 0101 mathematics, Companion quaternionic matrix, 01 natural sciences

File Description: application/xml; aplication/PDF

Access URL: https://www.sciencedirect.com/science/article/pii/S0898122101002358#!
https://www.sciencedirect.com/science/article/pii/S0898122101002358
https://estudogeral.sib.uc.pt/handle/10316/4646
https://estudogeral.sib.uc.pt/bitstream/10316/4646/1/file38fa5dda60ad4eb2b9ecf7b6db281718.pdf
https://hdl.handle.net/10316/4646

Computing Riemann matrices of algebraic curves

Authors: Bernard Deconinck, Mark van Hoeij

Source: Physica D: Nonlinear Phenomena. :28-46

Subject Terms: Computational aspects of algebraic curves, period matrix, Differentials on Riemann surfaces, Riemann surface, Maple 6, Software, source code, etc. for problems pertaining to functions of a complex variable, effective methods, Relationships between algebraic curves and integrable systems, 0101 mathematics, 01 natural sciences, Periodic solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/1624660
https://doi.org/10.1016/s0167-2789(01)00156-7
https://www.sciencedirect.com/science/article/pii/S0167278901001567
http://ui.adsabs.harvard.edu/abs/2001PhyD..152...28D/abstract

Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets: Generalized computation of Schröder iteration functions to motivate families of Julia and Mandelbrot-like sets

Authors: Drakopoulos, V, Argyropoulos, N, Bohm, A

Source: SIAM Journal on Numerical Analysis. 36:417-435

Subject Terms: Fatou set, General theory of numerical methods in complex analysis (potential theory, etc.), Software, source code, etc. for problems pertaining to functions of a complex variable, critical point, Julia set, Schröder's method, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 0101 mathematics, iteration, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1288897
https://doi.org/10.1137/s0036142997317365
https://epubs.siam.org/doi/abs/10.1137/S0036142997317365
https://pergamos.lib.uoa.gr/uoa/dl/object/3051600

The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence

Authors: T. E. Hull, Rudolf Mathon

Source: ACM Transactions on Mathematical Software. 22:261-280

Subject Terms: algorithm, Software, source code, etc. for problems pertaining to functions of a complex variable, multiple root, 01 natural sciences, quadratic convergence, polynomial zerofinder, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, iterative methods, Numerical computation of solutions to single equations, roots of a polynomial, 0101 mathematics, error analysis, polynomial rootfinders

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/toms/toms22.html#HullM96
https://dl.acm.org/doi/10.1145/232826.232830

The area of the Mandelbrot set

Authors: Ewing, John H., Schober, Glenn

Source: Numerische Mathematik. 61:59-72

Subject Terms: 4. Education, Software, source code, etc. for problems pertaining to functions of a complex variable, Julia set, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 16. Peace & justice, computation of coefficients, 01 natural sciences, Article, 510.mathematics, Coefficient problems for univalent and multivalent functions of one complex variable, area estimates, 0103 physical sciences, Mandelbrot set, 0101 mathematics

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://zbmath.org/38526
https://doi.org/10.1007/bf01385497
https://link.springer.com/article/10.1007/BF01385497?view=classic
https://link.springer.com/article/10.1007/BF01385497
https://eudml.org/doc/133610

A numerical comparison of integral equations of the first and second kind for conformal mapping

Authors: David K. Kahaner, John K. Hayes, Richard G. Kellner

Source: Mathematics of Computation. 29:512-521

Subject Terms: Schwarz-Christoffel-type mappings, 4. Education, Software, source code, etc. for problems pertaining to functions of a complex variable, 0101 mathematics, 10. No inequality, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/mcom/1975-29-130/S0025-5718-1975-0371036-8/S0025-5718-1975-0371036-8.pdf
https://zbmath.org/3477480
https://doi.org/10.2307/2005569
https://www.ams.org/journals/mcom/1975-29-130/S0025-5718-1975-0371036-8/home.html
https://www.ams.org/mcom/1975-29-130/S0025-5718-1975-0371036-8/S0025-5718-1975-0371036-8.pdf
http://www.osti.gov/scitech/biblio/5006665-numerical-comparison-integral-equations-first-second-kind-conformal-mapping
https://www.jstor.org/stable/pdfplus/2005569.pdf

Conformal mapping of the unit circle or of the upper half plane onto a polygon

Authors: W. Prochazka

Source: Computing. 31:155-172

Subject Terms: Schwarz-Christoffel-type mappings, polygonal boundaries, parameter problem, Schwarz-Christoffel formula, Software, source code, etc. for problems pertaining to functions of a complex variable, Conformal mappings of special domains, conformal transformation, graphic representation, Schwarz-Christoffel transformation, FORTRAN, IV-package, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3792489
https://doi.org/10.1007/bf02259911
https://link.springer.com/article/10.1007/BF02259911
https://dblp.uni-trier.de/db/journals/computing/computing31.html#Prochazka83

Experiments with a symbolic programming system for complex analysis

Authors: J. A. Campbell, R. J. Moore, J. G. Kent

Source: BIT. 16:241-256

Subject Terms: General theory of numerical methods in complex analysis (potential theory, etc.), 0103 physical sciences, Software, source code, etc. for problems pertaining to functions of a complex variable, 0102 computer and information sciences, Algorithms in computer science, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF01932266

A method of computing the complex probability function and other related functions over the whole complex plane

Authors: Sean J. McKenna

Source: Astrophysics and Space Science. 107:71-83

Subject Terms: Humlíček algorithm, Software, source code, etc. for problems pertaining to functions of a complex variable, complex Fresnel integrals, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), complex error function, 0101 mathematics, Voigt function, Software, source code, etc. for problems pertaining to special functions, complex Dawson's functions, 01 natural sciences

File Description: application/xml

Access URL: http://ui.adsabs.harvard.edu/abs/1984Ap&SS.107...71M/abstract
https://link.springer.com/article/10.1007/BF00649615

Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study: Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assistent study

Authors: Edward R Vrscay

Source: Mathematics of Computation. 46:151-169

Subject Terms: General theory of numerical methods in complex analysis (potential theory, etc.), fixed point, Local and nonlocal bifurcation theory for dynamical systems, bifurcation diagram, Software, source code, etc. for problems pertaining to functions of a complex variable, Julia sets, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 0101 mathematics, Topological dynamics, 01 natural sciences, iteration processes

File Description: application/xml

Access URL: https://www.ams.org/mcom/1986-46-173/S0025-5718-1986-0815837-5/S0025-5718-1986-0815837-5.pdf
https://www.ams.org/journals/mcom/1986-46-173/S0025-5718-1986-0815837-5/home.html
https://www.ams.org/mcom/1986-46-173/S0025-5718-1986-0815837-5/S0025-5718-1986-0815837-5.pdf

Formula manipulation in ALGOL 68 and application to Routh's algorithm

Authors: Kees Dekker

Source: Computing. 26:167-187

Subject Terms: Software, source code, etc. for problems pertaining to field theory, multistep methods, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Schur criterion, Software, source code, etc. for problems pertaining to functions of a complex variable, long integer arithmetic, Polynomials in real and complex fields: location of zeros (algebraic theorems), Routh's algorithm, 0101 mathematics, Algorithms in computer science, 01 natural sciences, location of the zeros of a complex polynomial

File Description: application/xml

An algorithm for winding numbers for closed polygonal paths

Authors: Kenneth O. Leland

Source: Mathematics of Computation. 29:554-558

Subject Terms: Finely holomorphic functions and topological function theory, General theory of numerical methods in complex analysis (potential theory, etc.), 4. Education, 0103 physical sciences, Software, source code, etc. for problems pertaining to functions of a complex variable, 0101 mathematics, Algorithms in computer science, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/mcom/1975-29-130/S0025-5718-1975-0373246-2/S0025-5718-1975-0373246-2.pdf
https://www.ams.org/mcom/1975-29-130/S0025-5718-1975-0373246-2/S0025-5718-1975-0373246-2.pdf
https://www.ams.org/journals/mcom/1975-29-130/S0025-5718-1975-0373246-2/home.html

Computer implementation of the Schwarz-Christoffel transformation

Authors: William Squire

Source: Journal of the Franklin Institute. 299:315-322

Subject Terms: Schwarz-Christoffel-type mappings, 0103 physical sciences, Software, source code, etc. for problems pertaining to functions of a complex variable, Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3498233
https://doi.org/10.1016/0016-0032(75)90170-2
https://www.sciencedirect.com/science/article/abs/pii/0016003275901702

On Bairstow’s method for the solution of polynomial equations: On Bairstow's method for the solution of polynomial equations

Authors: Kenneth W. Brodlie

Source: Mathematics of Computation. 29:816-826

Subject Terms: Software, source code, etc. for problems pertaining to real functions, 4. Education, Software, source code, etc. for problems pertaining to functions of a complex variable, Polynomials in real and complex fields: factorization, Polynomials in real and complex fields: location of zeros (algebraic theorems), 02 engineering and technology, 01 natural sciences, Real polynomials: location of zeros, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Numerical computation of solutions to single equations, 0101 mathematics, Algorithms in computer science

File Description: application/xml

Access URL: https://www.ams.org/mcom/1975-29-131/S0025-5718-1975-0381283-7/S0025-5718-1975-0381283-7.pdf
https://zbmath.org/3511509
https://doi.org/10.2307/2005292
https://www.jstor.org/stable/2005292
https://www.ams.org/mcom/1975-29-131/S0025-5718-1975-0381283-7/S0025-5718-1975-0381283-7.pdf
https://www.ams.org/journals/mcom/1975-29-131/S0025-5718-1975-0381283-7/home.html

Self-inverse fractals osculated by sigma-discs and the limit sets of inversion groups

Authors: Benoit B. Mandelbrot

Source: The Mathematical Intelligencer. 5:9-17

Subject Terms: limit set, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), algorithm, 05 social sciences, Software, source code, etc. for problems pertaining to functions of a complex variable, Kleinian group, Structure of modular groups and generalizations, arithmetic groups, 02 engineering and technology, Ergodic theory, fractals, computer graphics, Kleinian groups (aspects of compact Riemann surfaces and uniformization), Fricke-Klein text, 0502 economics and business, 0202 electrical engineering, electronic engineering, information engineering

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF03023620
https://link.springer.com/content/pdf/10.1007%2FBF03023620.pdf

Sequential and parallel complexity of approximate evaluation of polynomial zeros

Authors: Victor Y. Pan

Source: Computers & Mathematics with Applications. 14:591-622

Subject Terms: practical implementation, Analysis of algorithms and problem complexity, Software, source code, etc. for problems pertaining to functions of a complex variable, sequential and parallel algorithms, 0102 computer and information sciences, complex polynomial zeros, 01 natural sciences, upper bounds, Computational Mathematics, Computational Theory and Mathematics, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Modelling and Simulation, Numerical computation of solutions to single equations, 0101 mathematics, arithmetic and Boolean complexity

File Description: application/xml

Access URL: https://zbmath.org/4032925
https://doi.org/10.1016/0898-1221(87)90186-6
https://www.sciencedirect.com/science/article/pii/0898122187901866
https://core.ac.uk/display/22969160
http://comet.lehman.cuny.edu/vpan/pdf/pan61.pdf