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Iterative Methods for Nonlinear Equations

Iterative Methods for Nonlinear Equations is a research topic within Numerical Analysis. Science Explorer counts 17k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the convergence analysis and improvement of iterative methods, particularly Newton's method, for solving nonlinear equations. It explores higher-order methods, quadrature formulas, local convergence in Banach spaces, and derivative-free approaches to handle multiple roots.

  • Newton's Method
  • Iterative Methods
  • Convergence Analysis
  • Nonlinear Equations
  • Higher-Order Methods
  • Quadrature Formulas
  • Local Convergence
  • Multiple Roots
  • Derivative-Free Methods
  • Banach Spaces
Research works
17k
fractional, since 1950
In the world top 10%
1.7k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-1%
the tick is no change
Largest producer
India
23% of the 10 largest, 2022-now
Iterative Methods for Nonlinear Equations

Which countries lead Iterative Methods for Nonlinear Equations research?

By volume, India and China publish the most (396 and 367 works in 2022-now).

By volume, 2022-now

  1. 1 India 396 works
  2. 2 China 367 works
  3. 3 United States 176 works
  4. 4 Türkiye 138 works
  5. 5 Iran 129 works
  6. 6 Iraq 127 works
  7. 7 Saudi Arabia 121 works
  8. 8 Pakistan 86 works
  9. 9 Russia 80 works
  10. 10 Nigeria 67 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

India: 23.5%China: 21.8%United States: 10.5%Türkiye: 8.2%6 others listed: 36.2%23%largest
India396 · 23.5%China367 · 21.8%United States176 · 10.5%Türkiye138 · 8.2%6 others listed610 · 36.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Iterative Methods for Nonlinear Equations research?

By volume in 2022-now, University of Mosul publishes the most Iterative Methods for Nonlinear Equations research, followed by Cameron University and Islamic Azad University, Tehran.

By volume, 2022-now

  1. 1 University of MosulIraq 24 works
  2. 2 Cameron UniversityUnited States 22 works
  3. 3 Islamic Azad University, TehranIran 19 works
  4. 4 Russian Academy of SciencesRussia 19 works
  5. 5 Universitat Politècnica de ValènciaSpain 16 works
  6. 6 National Institute of Technology KarnatakaIndia 15 works
  7. 7 King Saud UniversitySaudi Arabia 14 works
  8. 8 King Abdulaziz UniversitySaudi Arabia 13 works
  9. 9 University of BaghdadIraq 12 works
  10. 10 Zarqa UniversityJordan 12 works

Who are the leading researchers in Iterative Methods for Nonlinear Equations?

The most-cited researchers publishing on Iterative Methods for Nonlinear Equations include R. W. L. Jones, Stephen Boyd and Tasawar Hayat.

  1. 1 R. W. L. Jones United Kingdom 189k citations
  2. 2 Stephen Boyd United States 142k citations
  3. 3 Tasawar Hayat Pakistan 135k citations
  4. 4 William H. Press United States 119k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Iterative Methods for Nonlinear Equations?

The most cited paper in Iterative Methods for Nonlinear Equations is "On the limited memory BFGS method for large scale optimization" (Dong C. Liu, Jorge Nocedal, 1989), with 8,813 citations. Next come "Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions" (7,523) and "A Limited Memory Algorithm for Bound Constrained Optimization" (6,417).

Most cited papers
#PaperReleasedCitations
1 On the limited memory BFGS method for large scale optimization Dong C. Liu, Jorge Nocedal · Mathematical Programming Aug 1989 8,813
2 Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions Jeffrey C. Lagarias, James A. Reeds, Margaret H. Wright et al. · SIAM Journal on Optimization 1998 7,523
3 A Limited Memory Algorithm for Bound Constrained Optimization Richard H. Byrd, Peihuang Lu, Jorge Nocedal et al. · SIAM Journal on Scientific Computing Sep 1995 6,417
4 The method of moving asymptotes—a new method for structural optimization Krister Svanberg · International Journal for Numerical Methods in Engineering Feb 1987 5,593
5 Function minimization by conjugate gradients Roger Fletcher · The Computer Journal Feb 1964 4,962
All 100 most cited papers, with filters and sorting

Where is Iterative Methods for Nonlinear Equations research done?

The largest centres of Iterative Methods for Nonlinear Equations research in 2022-now are Riyadh (Saudi Arabia), Tehran (Iran), Baghdad (Iraq) and Moscow (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Lawton.

Largest cities, 2022-now

  1. 1 RiyadhSaudi Arabia 37 works
  2. 2 TehranIran 35 works
  3. 3 BaghdadIraq 30 works
  4. 4 MoscowRussia 29 works
  5. 5 BeijingChina 28 works
  6. 6 MosulIraq 25 works
  7. 7 AnkaraTürkiye 23 works
  8. 8 LawtonUnited States 22 works
  9. 9 JeddahSaudi Arabia 20 works
  10. 10 ValenciaSpain 19 works

Where it is the local speciality

  1. LawtonUS · 21.6 works1095×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Iterative Methods for Nonlinear Equations than the world average.

See Iterative Methods for Nonlinear Equations on the map

Where is the best place to study Iterative Methods for Nonlinear Equations?

Among universities, judged by research, Zarqa University, Al-Balqa Applied University and Abdul Wali Khan University Mardan score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 21.12%fractional works in this field (log) →share of work in the world top 10% →Al-Balqa Applied Uni…Abdul Wali Khan Univ…Thi Qar UniversityZarqa University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Zarqa UniversityJordan 59.924.7%61.6×12 +750.8%
2Al-Balqa Applied UniversityJordan 58.841.8%34.3×9 -10.1%
3Abdul Wali Khan University MardanPakistan 54.131.5%42.1×9 +37.7%
4Thi Qar UniversityIraq 51.027.0%32.2×11 +57.7%
5China Medical UniversityTaiwan 50.831.6%29.6×10 -28.7%
6University of MosulIraq 49.80.4%28.7×24 +17.9%
7King Saud UniversitySaudi Arabia 46.55.4%6.0×14 +66.3%
8Bohai UniversityChina 45.423.6%47.8×11 +228.1%
9Universitat Politècnica de ValènciaSpain 42.79.3%19.1×16 -17.4%
10King Abdulaziz UniversitySaudi Arabia 42.615.9%10.2×13 -23.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Iterative Methods for Nonlinear Equations, country by country

Is Iterative Methods for Nonlinear Equations research growing?

Output in 2022-2025 was 1% lower than in 2018-2021, peaking in 2021.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Iterative Methods for Nonlinear Equations as a percentage of every work published that year, 0.012% in 2024.

still counting0.020%0.040%Iterative Methods for Nonlinear Equations0.0097% in 202519801990200020102020

Fractional works of Iterative Methods for Nonlinear Equations over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Iterative Methods for Nonlinear Equations10.2% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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