About the Laboratory
Mission
Welcome to the Math-oriented Approach Laboratory (M.A.L.).
This site is a personal hobby project where the administrator explores "equations of the world," solving them using numerical methods and archiving the convergence processes and results.
Mathematics is the purest language for describing the natural world and engineering challenges. I aim to rediscover its beauty and record the process of unraveling complex problems.
Research Themes
Based on knowledge of numerical analysis from my student days, I publish information centered on the following topics:
- ・Solving Benchmark Problems
Tackling famous nonlinear equations and difficult benchmark problems using various approaches. - ・Implementation of Numerical Algorithms
Explanations and implementation experiments of algorithms used to derive solutions, such as the Homotopy method and Newton's method. - ・Utilizing Tools as Solvers
Circuit simulators like SPICE are treated here not as circuit design tools, but strictly as "excellent solvers for large systems of equations," verifying and utilizing their computational capabilities.
Profile
Dr. WataWata
Ph.D. in Engineering
Firmware Development Engineer / Numerical Analysis Enthusiast
I work in embedded software and firmware development. I specialized in numerical analysis as a student and earned a Ph.D. Today, I apply the mathematical thinking I developed there to areas such as algorithm design for firmware.
At work, I build things that operate within hardware constraints; as a hobby, I explore equations and numerical problems. Spending time with mathematics, a little removed from day-to-day engineering, is a welcome change of pace.
Outside mathematics and programming, I have also practised Kendo for many years. Alongside notes on mathematics and technology, this site gradually collects calculators I wanted to use myself and practical tools related to Kendo.
🧬 Ongoing Project
Currently developing the original hybrid optimization solver "MAL-Seeker".
Current Development: Project Bellatrix V1.0.4
Origin of "M.A.L."
Formal Name: Math-oriented Approach Laboratory
While holding the philosophy of "approaching the essence of problems with a Math-oriented approach," there is actually another meaning important to me.
The acronym "M.A.L." is taken from the name of my beloved dog, "Maru", who once supported my life.
Even when facing complex and difficult problems (equations), I want to solve them simply, with charm and persistence just like Maru. With that wish, I named this place M.A.L.
Update History
| 2026.10.03 | Added Owada Kenyukai to the Kendo Associations section of Links. |
| 2026.10.03 | Added Fourier Transform to Methods, with 5 Hz and 12 Hz waveform examples, frequency spectra, and a visual explanation of the DFT and FFT. |
| 2026.10.03 | Added Genetic Algorithm to Methods, illustrating selection, crossover, mutation, and the changing candidate population across generations. |
| 2026.10.02 | Set Galaxy, Classic White, Research Notebook, Handheld Game, and Halloween Night to rotate daily in Japan time, and added the theme name beneath the home-page logo. |
| 2026.09.30 | Added Excel output to the Kendo Order Sheet Maker. The current text, borders and paper settings can now be saved as an editable workbook built on a 5 mm grid. |
| 2026.09.29 | Added the QR Code Reader to Tools. It reads QR codes locally in the browser from a camera, image file, drag and drop, or a pasted screenshot. |
| 2026.09.29 | Added the Differential Equation Visualizer as the latest home-page feature. The home page now shows one feature, with earlier selections collected in a new feature archive. |
| 2026.09.28 | Added the Kendo Order Sheet Maker with three-, five- and seven-person layouts, millimetre paper settings, direct editing, output line visibility controls, split printing, PDF, PNG, SVG and template output. |
| 2026.09.27 | Added Dating Was TCP; Marriage Became UDP to Insights, using fictional chats to explain connections, ACKs, retransmission, ordering, packet loss, and suitable uses. |
| 2026.09.27 | Added Big-Endian and Little-Endian to Insights, with diagrams for integer and floating-point byte layout, identification tips, and a practical decoding checklist. |
| 2026.09.26 | Added the Differential Equation Visualizer with five ODE methods, solution and error graphs, Newton iteration information, all-method comparison and method equations. |
| 2026.09.26 | Added the Numerical Integration Playground with five integration rules, high-accuracy reference and error values, and visual approximation shapes. |
| 2026.09.25 | Added monthly birthstones from the 2021 Japanese list and a representative monthly birth flower to the Age & Date Calculator. |
| 2026.09.25 | Added a Finance & Life Planning category with the Loan Calculator and Savings Calculator, including borrowing capacity, prepayment comparison, target calculations, rate scenarios and inflation adjustment. |
| 2026.09.25 | Added the Percentage Calculator with ten guided calculations for amounts, changes, targets, original values, tax, profit margin and repeated changes. |
| 2026.09.25 | Added PID Playground with live Kp, Ki and Kd controls, first-order response and output graphs, rise time, overshoot, settling time and steady-state error. |
| 2026.09.20 | Expanded the Age Calculator with Gregorian/Japanese era birth-date results, duration calculation, and date addition or subtraction. |
| 2026.09.20 | Added the Function Plotter for graphing up to two functions and inspecting numerically detected intersections with coordinate tooltips. |
| 2026.09.20 | Added the Statistics Calculator with selectable histogram, normal-curve overlay, mean ± SD error bar and box-plot views. |
| 2026.09.18 | Added Polynomial Regression & Graph. Select two columns from up to five series and 20 rows, then calculate a degree 1–5 fit, graph, R² and RMSE entirely in the browser. Data-point and curve colours can be changed, and the graph can be copied as an image. |
| 2026.09.14 | MAL-Seeker updated for Bellatrix V1.0.4, presenting the current problem scope, search process, and published verification records without exposing implementation details. |
| 2026.09.13 | PHCpack Benchmark Test 4: Added results for 18 systems in both languages, including 429 matched roots for pole27sys and the incomplete 461/462 pole34sys result; updated the sitemap. |
| 2026.09.11 | Added three Field Notes stories: “Congratulations”—Is That Right?、Manners Matter, Too、“Stay Calm,” Says AI。 |
| 2026.09.11 | Launched Field Notes with “Still Looping Today” in Japanese and English, under Everyday Life with Someone. Added a home-page illustration and navigation links. |
| 2026.09.10 | Added Featured | Explore Mathematics to the home page, highlighting the SPICE Rosenbrock analysis. Organized archive pages by subject. |
| 2026.09.09 | v1.0.74: Added Maru and Dr.WataWata as M.A.L. characters. |
| 2026.09.05 | v1.0.56: Expanded the Electrical Circuit Calculator with AC impedance, series/parallel RLC resonance, voltage- and power-ratio dB conversion, and inverting, non-inverting, summing and differential op-amp calculations. RLC impedance now includes magnitude and phase frequency-response charts. |
| 2026.09.05 | v1.0.55: Added the Electrical Circuit Calculator as TOOL 05. It calculates Ohm's law and power, series/parallel resistors and capacitors, RC time constants, RC/CR cutoff frequency, voltage dividers and LED current-limiting resistors with selectable units and visible formulas. |
| 2026.09.04 | v1.0.54: Added a Homotopy mode choice between stopping at the λ=1 solution and continuing beyond λ=1. Normal mode now ends on the corrected point with λ exactly equal to 1. Continued tracking has an adjustable λ search range to avoid unnecessarily long paths. |
| 2026.09.04 | v1.0.53: Replaced Homotopy tracking in the Nonlinear Solver Visualizer with a pseudo-arclength predictor-corrector. It can follow folds without forcing λ to increase, continue beyond λ=1 and record distinct corrected intersections as solutions. Added first-solution mode, arclength/step/divergence/closed-path safeguards and a detected-solutions table. |
| 2026.09.02 | v1.0.52: Added Custom Equation to the Nonlinear Solver Visualizer. Users can enter up to ten equations using x1–x10, arithmetic, powers and common mathematical functions, then run Newton, Linear Homotopy or Newton Homotopy. Syntax, variable-range and domain errors plus sample inputs are included. |
| 2026.09.02 | v1.0.51: Made the Nonlinear Solver Visualizer playback controller sticky so previous, play/pause, next and speed controls remain available while viewing any chart. The current Step and λ are also shown in the controller. |
| 2026.09.02 | v1.0.50: Replaced the visualizer's three-axis projection with a selectable two-dimensional chart. The vertical axis now shows iteration count for Newton and λ for Homotopy, with clearer explanations of axes, points, lines and colours. |
| 2026.09.02 | v1.0.49: Added Nonlinear Solver Visualizer as TOOL 04 with up to ten variables, Newton, Linear/Newton Homotopy, predictor-corrector steps, three-axis projections, variable histories and residual histories. |
| 2026.09.01 | v1.0.48: Renumbered Radix Converter as TOOL 03, Kendo Scoreboard as TOOL 04 and Tournament Maker as TOOL 05 to match their order in Tools. |
| 2026.09.01 | v1.0.47: Added IEEE 754 binary16 (half precision), big-/little-endian byte display and fixed-point Q formats to Radix Converter, including resolution, range and quantisation error. |
| 2026.09.01 | v1.0.46: Expanded the IEEE 754 tools with direct bit editing, binary conversion, normalisation and biasing steps, adjacent representable values and ULP. |
| 2026.09.01 | v1.0.45: Added Radix Converter to Tools, covering bases 2, 8, 10 and 16, fractions and recurring fractions, two's complement, binary32/binary64 IEEE 754, reverse conversion and rounding error. |
| 2026.09.01 | v1.0.44: Added a return-to-home link above the title on the About, Books, Equations, Insights, Links, Methods, Projects and Tools section pages. |
| 2026.09.01 | v1.0.43: Added a return-to-section link above the title on every detail page in Equations, Insights, Methods, Projects and Tools. |
| 2026.09.01 | v1.0.42: Added Learning Numerical Programming through C to Books, highlighting its uncommon inclusion of the homotopy method. |
| 2026.09.01 | v1.0.41: Split the combined jQuery and JavaScript entry in Books into individual cards and added a separate introduction for each title. |
| 2026.09.01 | v1.0.40: Added Circuit Simulation and Modeling with Python to Books, with links to the publisher and Amazon. |
| 2026.08.31 | v1.0.39: Added the Tournament Maker web app introduction to Tools, covering bracket generation, match results, Excel/PDF exports, iPhone/Android home-screen setup, and saving and sharing notes. |
| 2026.08.31 | v1.0.38: Added the Kendo Scoreboard web app introduction to Tools, including its background and iPhone/Android home-screen instructions. Added shared and per-tool usage notes. |
| 2026.08.31 | v1.0.37: Added Amazon links for eight more books. Separated the jQuery and JavaScript purchase options, added edition and search-link notes, and corrected publisher information. |
| 2026.08.31 | v1.0.36: Introduced publisher and Amazon links for Numerical Recipes in Books as an affiliate trial, with an advertising disclosure. |
| 2026.08.30 | v1.0.35: Clarified the calculation-method labels for water vapour and dew point. |
| 2026.08.30 | v1.0.34: Added calculation of relative humidity and water vapour from dew point. |
| 2026.08.30 | v1.0.33: Added water-vapour and dew-point calculation to the category menu. |
| 2026.08.30 | v1.0.32: Added pressure conversion plus water-vapour and dew-point calculations. |
| 2026.08.30 | v1.0.31: Added zodiac results to the Age Calculator and improved the Unit Converter input order. |
| 2026.08.30 | v1.0.30: Added Japanese era-date input from Meiji through Reiwa to the Age Calculator. |
| 2026.08.30 | v1.0.29: Added a Tools section with age calculation and unit conversion. |
| 2026.08.28 | v1.0.28: Added articles on comparing price plans and measuring height with shadows to Insights & Essays. |
| 2026.08.28 | v1.0.27: Added “Nonlinear Equations Are Not Just One Kind of Problem” to Insights & Essays. |
| 2026.08.13 | v1.0.26: Added Bistable Latch Circuit and Five-Node Tunnel-Diode Ladder to the Equations Archive. |
| 2026.08.13 | v1.0.25: Added PHCpack Benchmark Test 3 to the Equations Archive. |
| 2026.07.30 | v1.0.24: Added PHCpack Benchmark Test 2 to the Equations Archive. |
| 2026.06.15 | v1.0.23: Added PHCpack1 to Equations Archive. |
| 2026.05.15 | v1.0.22: Added Fixed Point Problem (10D) to Equations Archive. |
| 2026.05.09 | v1.0.21: Added Katsura Equations (5D) to Equations Archive. |
| 2026.05.06 | v1.0.20: Added Multivariable Quadratic (MQ) Problem to Equations Archive. |
| 2026.05.03 | v1.0.19: Added Discrete Boundary Value Problem to Equations Archive. |
| 2026.05.01 | v1.0.18: Added Neurophysiology Model (10D) to Equations Archive. |
| 2026.05.01 | v1.0.17: Added Non-Isothermal CSTR to Equations Archive. |
| 2026.04.05 | v1.0.16: Added Ackley Function (20D) to Equations Archive. |
| 2026.04.01 | v1.0.15: Added Schwefel Function (5D) to Equations Archive. |
| 2026.03.28 | v1.0.14: Added new benchmark problems to Equations Archive. |
| 2026.03.27 | v1.0.13: Launched the new "Projects" section. |
| 2026.03.27 | v1.0.12: Added a 10-variable system to Equations Archive. |
| 2026.03.20 | v1.0.11: Added Rastrigin Function to Equations Archive. |
| 2026.03.01 | v1.0.10: Added Himmelblau's system to Equations Archive. |
| 2026.02.19 | v1.0.9: Added Wilkinson's Polynomial to Equations Archive. |
| 2026.02.07 | v1.0.8: Added Multiphase Equilibrium to Equations Archive. |
| 2026.02.03 | v1.0.7: Added Scarf's Economic Equilibrium Problem to Equations Archive. |
| 2026.01.31 | v1.0.6: Added Chandrasekhar's H-equation to Equations Archive. |
| 2026.01.23 | v1.0.5: Added Linear Complementarity Problem to Equations Archive. |
| 2026.01.16 | v1.0.4: Added All-Solution Search via Homotopy Method to Equations Archive. |
| 2026.01.10 | v1.0.3: Added Linear Programming Problem to Equations Archive. |
| 2026.01.03 | v1.0.2: Added 1D Heat Conduction Equation to Equations Archive. |
| 2025.12.30 | v1.0.1: Added new benchmark problems to Equations Archive. |
| 2025.12.10 | v1.0.0: Opened Math-oriented Approach Laboratory - M.A.L. |
Disclaimer
While we strive for accuracy regarding the programs, formulas, and analysis results presented on this site, we do not guarantee their completeness or accuracy.
The laboratory (administrator) assumes no responsibility for any damages arising from the use of information on this site.